## One-Dimensional Motion Multiple Choice Questions And Answers

**Question 1. A particle moves from A to B along the semicircle of radius 1.0 m in 1s. The magnitude of the average velocity of the particle is**

- 3.14 m · s
^{-1} - 2.0 m· s
^{-1} - 1.0m· s
^{-1} - Zero

**Answer:** 2. 2.0 m· s^{-1}

**Question 2. A vehicle is moving with a uniform speed 18 km · h ^{-1}. The distance covered by it in 1 s is**

- 18m
- 5m
- 10m
- 1m

**Answer:** 2. 5m

**Question 3. Distance travelled by a particle in motion is directly proportional to the square of the time of travel. In this stage, the acceleration of the particle is**

- Increasing
- Decreasing
- Zero
- Constant

**Answer:** 4. Constant

**Question 4. A person covers half of his path at a speed of 30 km · h ^{-1} and the remaining half at 40 km · h^{-1}. His average speed is**

- 35 km · h
^{-1} - 60 km · h
^{-1} - 34.3 km · h
^{-1} - 50km · h
^{-1}

**Answer:** 3. 34.3 km · h^{-1}

**Question 5. Starting from rest, a car moves for some time with a constant acceleration x and then with a constant retardation y and finally, it comes to rest. If the car is in motion for a total time t, the maximum velocity of the car is**

- \(\frac{x y}{x+y} \cdot t\)
- \(\frac{x y}{x-y} \cdot t\)
- \(\frac{x^2 y^2}{x^2+y^2} \cdot t\)
- \(\frac{x^2 y^2}{x^2-y^2} \cdot t\)

**Answer:** 1. \(\frac{x y}{x+y} \cdot t\)

**Question 6. Displacement (x) and time (t) of a particle in motion are related as x = at+ bt² -ct³ where a, b and c are constants. The velocity of the particle when its acceleration becomes zero is**

- \(a+\frac{a^2}{c} s\)
- \(a+\frac{b^2}{2 c}\)
- \(a+\frac{b^2}{3 c}\)
- \(a+\frac{b^2}{4 c}\)

**Answer:** 3. \(a+\frac{b^2}{3 c}\)

**Question 7. The motion of a particle is described by the equation v = at. The distance travelled by the particle in the first 4 s**

- 4a
- 8a
- 12a
- 6a

**Answer:** 2. 8a

**Question 8. A particle starting from rest with constant acceleration travels a distance x in the first 2s and a distance y in the next 2s. then**

- y = 3x
- y = 2x
- y = x
- y = 4x

**Answer:** 1. y = 3x

**Question 9. The displacement of a particle is given by y = a + bt + ct² – dt ^{4}. The initial velocity and acceleration are respectively**

- b, -4d
- b, 2c
- -b, -2c
- 2c, -4c

**Answer:** 2. b, 2c

**Question 10. The displacement of a particle, starting from rest (at t = 0) is given by s = 6t² – t³. The time in seconds at which the particle obtains zero velocity again is**

- 2
- 4
- 6
- 8

**Answer:** 2. 4

**Question 11. A car starts from rest and travels a distance s with a uniform acceleration f; then it travels with uniform velocity for a time f; and at last, comes to rest with a uniform retardation \(\frac{f}{2}\). If the total distance travelled is 5 s. Then**

- s = ft
- s = \(\frac{1}{2}\)ft²
- s = \(\frac{1}{4}\)ft²
- s = \(\frac{1}{6}\)ft²

**Answer:** 2. s = \(\frac{1}{2}\)ft²

**Question 12. Two stations A and B are 2 km apart. A train moves at first with uniform acceleration a _{1 }and then with a uniform retardation a_{2} to travel the distance AB in 4 min. Then**

- \(a_1+a_2=2 a_1 a_2\)
- \(\frac{1}{a_1}+\frac{1}{a_2}=\frac{1}{2}\)
- \(a_1+a_2=4 a_1 a_2\)
- \(a_1+a_2=2 \sqrt{a_1 a_2}\)

Hint: \(2=s_1+s_2=\frac{v^2}{2 a_1}+\frac{\nu^2}{2 a_2}=\frac{v^2}{2}\left(\frac{1}{a_1}+\frac{1}{a_2}\right)=\frac{v^2}{2}\left(\frac{a_1+a_2}{a_1 a_2}\right)\)

or, \(v^2=\frac{4 a_1 a_2}{a_1+a_2}\)

Also, \(4=t_1+t_2=\frac{v}{a_1}+\frac{v}{a_2}=v \frac{a_1 a_2}{a_1+a_2}\)

or, v = \(\frac{4 a_1 a_2}{a_1+a_2} or, v^2=\left(\frac{4 a_1 a_2}{a_1+a_2}\right)^2\)

∴ \(\frac{4 a_1 a_2}{a_1+a_2}=\left(\frac{4 a_1 a_2}{a_1+a_2}\right)^2\)

or, \(1=\frac{4 a_1 a_2}{a_1+a_2}\)

or, \(a_1+a_2=4 a_1 a_2\)

**Answer:** 3. \(a_1+a_2=4 a_1 a_2\)

**Question 13. A car moves with a uniform velocity of 36 km · h ^{-1} on a straight road. Then it attains a uniform acceleration and doubles its velocity in 10 s. The radius of the wheel of the car is 25 cm. The number of complete rotations of the wheel in those 10 s would be about**

- 84
- 95
- 126
- 135

**Hint:** u = 36 km · h^{-1} = 10 m/s; v – 2u = 20 m/s;

a = \(\frac{v-u}{t}=\frac{20-10}{10}=1 \mathrm{~m} / \mathrm{s}^2\)

∴ Distance travelled in 10 s, s = 10 x 10 + \(\frac{1}{2}\) x 1 x 10² = 150 m

Number of rotations = \(\frac{s}{2 \pi r}=\frac{150}{2 \times 3.14 \times 0.25}=95.54\)

**Answer:** 2. 95

**Question 14. Two scooters start at an interval of 1 min between them, each moving with a uniform acceleration of 0. 4 m/s². How much later the distance between them would be 4.2 km?**

- 195 s
- 205 s
- 175 s
- 250 s

**Hint: **\(s_1-s_2=\frac{1}{2} a t^2-\frac{1}{2} a\left(t-t^{\prime}\right)^2\left(t^{\prime}=1 \mathrm{~min}=60 \mathrm{~s}\right)\)

= \(\frac{1}{2} a\left[t^2-\left(t^2+t^{\prime 2}-2 t t^{\prime}\right)\right]=a t t^{\prime}-\frac{1}{2} a t^{\prime 2}\)

or, \(t=\frac{1}{a t^{\prime}}\left\{\left(s_1-s_2+\frac{1}{2} a t^{\prime 2}\right)\right\}=\frac{s_1-s_2}{a t^{\prime}}+\frac{t^{\prime}}{2}\)

= \(\frac{4.2 \times 1000}{0.4 \times 60}+\frac{60}{2}=205 \mathrm{~s}\)

**Answer:** 2. 205 s

**Question 15. A passenger in a train with a speed 72 km/h observed another train coming from the opposite direction with a speed of 32.4 km/h. What is the length of the second train if it crosses the passenger in 10 s?**

- 300 m
- 110 m
- 2.9 m
- 290 m

**Answer:** 4. 290 m

**Question 16. A runner wins a race in front of another runner. The uniform accelerations of were a _{1} and a_{2} respectively. The time taken by the first runner is less by t, and the velocity at the finishing point is higher by v, relative to the second runner. Then**

- \(t=v \sqrt{a_1 a_2}\)
- \(v=t \sqrt{a_1 a_2}\)
- \(a_1=a_2 \sqrt{v t}\)
- \(\frac{1}{v}=t \sqrt{a_1 a_2}\)

**Hint:** \(s=\frac{1}{2} a_1 t_1^2\) = \(\frac{1}{2} a_2\left(t_1+t\right)^2\)

or, \(\frac{a_1}{a_2}=\left(\frac{t_1+t}{t_1}\right)^2\)

or, \(1+\frac{t}{t_1}=\sqrt{\frac{a_1}{a_2}}\)

Again, \(v=v_1-v_2\)

= \(a_1 t_1-a_2\left(t_1+t\right)=\left(a_1-a_2\right) t_1-a_2 t\)

= \(\left(a_1-a_2\right) \frac{t \sqrt{a_2}}{\sqrt{a_1}-\sqrt{a_2}}-a_2 t\)

= \(\left(\sqrt{a_1}+\sqrt{a_2}\right) \sqrt{a_2} t-a_2 t\)

= \(\sqrt{a_2} t\left(\sqrt{a_1}+\sqrt{a_2}-\sqrt{a_2}\right)=\sqrt{a_2} t \sqrt{a_1}\)

or, \(v=t \sqrt{a_1 a_2}\)

**Answer:** 2. \(v=t \sqrt{a_1 a_2}\)

Also, note that the expressions other than 2 do not satisfy the principle of dimensional homogeneity.

**Question 17. A body is thrown vertically upwards at 40 m · s ^{-1}. After some time the body returns to the initial point at the same speed. The average velocity of the body for the motion is**

- 45 m · s
^{-1} - 40 m · s
^{-1} - 48 m · s
^{-1} - Zero

**Answer:** 4. Zero

**Question 18. A body freely falling from rest has a velocity v after it falls through a height of h. The distance it has to fall down for its velocity to become 2 v is**

- 4 h
- 6 h
- 8 h
- 10 h

**Answer:** 1. 4h

**Question 19. A ball is thrown vertically upward with a speed v from a height h above the ground. The time taken for the ball to hit the ground is**

- \(\frac{v}{g} \sqrt{1-\frac{2 h g}{v^2}}\)
- \(\sqrt{1+\frac{2 h g}{v^2}}\)
- \(\frac{v}{g}\left[1+\sqrt{1+\frac{2 h g}{v^2}}\right]\)
- \(\frac{v}{g} \sqrt{1+\frac{2 h g}{v^2}}\)

**Answer:** 3. \(\frac{v}{g}\left[1+\sqrt{1+\frac{2 h g}{v^2}}\right]\)

**Question 20. A body A is thrown up vertically from the ground with a velocity v _{0} and another body B is simultaneously dropped from a height H. They meet at a height \(\frac{H}{2}\), if v_{0} is equal to**

- \(\sqrt{2 g H}\)
- \(\sqrt{g H}\)
- \(\frac{1}{2} \sqrt{g H}\)
- \(\sqrt{\frac{2 g}{H}}\)

**Answer:** 2. \(\sqrt{g H}\)

**Question 21. A stone is dropped from a height of h. Another stone is thrown simultaneously in the vertical direction so as to rise to a height of 4 h. How much later would the two stones cross each other?**

- \(\sqrt{\frac{h}{8 g}}\)
- \(\sqrt{8 g h}\)
- \(\sqrt{2 g h}\)
- \(\sqrt{\frac{h}{2 g}}\)

**Answer:** 1. \(\sqrt{\frac{h}{8 g}}\)

**Question 22. A stone is falling freely. The distance travelled in the last second is equal to that travelled in the first three seconds. The time spent by the stone in the air is**

- 6s
- 5s
- 7s
- 4s

**Answer:** 2. 5s

**Question 23. A stone is thrown vertically upwards from some high point P. The velocity of the stone at a height h above P is half that at a depth h below P. The maximum height attained by the stone is**

- \(\frac{7}{3}\)h
- \(\frac{5}{3}\)h
- \(\frac{7}{5}\)h
- \(\frac{9}{7}\)h

**Answer:** 2. \(\frac{5}{3}\)h

**Question 24. A hail drop is falling freely due to gravity. It travels distances h _{1}, h_{2} and h_{3} respectively in the first, second and third seconds of motion. The relation among h_{1}, h_{2} and h_{3} is**

- \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\)
- \(h_2=3 h_1\) and \(h_3=h_2\)
- \(h_1=h_2=h_3\)
- \(h_1=2 h_2=3 h_3\)

**Answer:** 1. \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\)

**Question 25. A parachute is dropped from an aeroplane. The parachute opens after 10 s and then comes down with a uniform retardation of 2.5 m · s ^{-2}. If the aeroplane was at a height of 2.495 km and g = 10 m· s^{-2}, then the velocity at which the parachute touches the ground is**

- 2.5 m · s
^{-1} - 7.5 m · s
^{-2} - 5m · s
^{-2} - 10m · s
^{-2}

**Answer:** 3. 5m · s^{-2}

**Question 26. A body falls freely from a certain height. It takes times t _{1} and t_{2} to travel the first and the last half distances, respectively. Then**

- (√2 +1)t
_{1}= t_{2} - (√2 +1)t
_{2}= t_{1} - (√2 -1)t
_{1}= t_{2} - (√2 +1)t
_{2}= t_{1}

**Answer:** 3. (√2 -1)t_{1} = t_{2}

**Question 27. A small cube falls from rest along a frictionless inclined plane. If this distance travelled between times t=n-1 and t=n be \(s_n\), then the value of \(\frac{s_n}{s_{n+1}}\) is**

- \(\frac{2 n-1}{2 n}\)
- \(\frac{2 n+1}{2 n-1}\)
- \(\frac{2 n-1}{2 n+1}\)
- \(\frac{2 n}{2 n+1}\)

**Hint: The acceleration is less than g, but still it is uniform, say a. So, s _{t} = \(\frac{1}{2}\)a(2t-1). Calculate s_{n}, s_{n+1} and take the ratio.**

**Answer:** 3. \(\frac{2 n-1}{2 n+1}\)

**Question 28. For a freely falling body, the acceleration-time graph is a**

- Straight line parallel to the acceleration axis
- Straight line parallel to the time axis
- A straight line passing through the origin
- Parabola passing through the origin

**Answer:** 2. Straight line parallel to the time axis

**Question 29. The area under the velocity-time graph for a particle in a given interval of time represents**

- Velocity
- Acceleration
- Work done
- Displacement

**Answer:** 4. Displacement

**Question 30. Which one of the following displacement time graphs represents the one-dimensional motion of a particle?**

**Answer:** 4

**Question 31. The displacement of a particle at different intervals of time is tabulated below**

**Which one of the graphs correctly represents the motion of the particle?**

**Answer:** 3

**Question 32. A position-time graph for motion with zero acceleration is**

**Answer:** 3

**Question 33. The displacement-time graph of two moving particles makes angles of 30° and 45° with the X-axis. The ratio of their velocities is**

- 3:2
- 1:1
- 1:2
- 1:3

**Answer:** 4. 1:3

**Question 34. The displacement-time graphs of two particles moving along the X-axis. We can say that**

- Both particles are uniformly accelerated
- Both the particles are uniformly retarded
- Particle (1) is uniformly accelerated while particle (2) is uniformly retarded
- Particle (1) is uniformly retarded while particle (2) is uniformly accelerated

**Answer:** 3. Particle (1) is uniformly accelerated while particle (2) is uniformly retarded

**Question 35. The acceleration-time graph of a particle is shown which of the following would be the velocitytime graph?**

**Answer:** 4

**Question 36. On an acceleration-time graph, the area under the graph represents**

- Distance Travelled
- Active Force
- Change Of Acceleration
- Change Of Velocity

**Answer:** 4. Change Of Velocity

**Question 37. Shows the velocity-time graph of a stone thrown vertically upwards with a velocity of 30 m · s ^{-1}. The maximum height attained by the stone is**

- 30 m
- 45 m
- 60 m
- 90 m

**Answer:** 2. 45 m

**Question 38. A ball is dropped on a fixed horizontal plane from a certain height. After recoil from the plane, it rises to a lower height. The correct nature of the height-time graph is**

**Answer:** 3

**Question 39. The equation of motion of a particle in two-dimensional space is x = 5t²+ 2; y = 2t² + 5. The path traced out is**

- Parabolic
- Circular
- A straight line
- Hyperbolic

**Answer:** 3. A straight line

**Question 40. In a three-dimensional space of zero gravity, the equation of motion of a particle is**

- One-dimensional
- Two-dimensional
- Three-dimensional
- Four-dimensional

**Answer:** 1. One-dimensional

**Question 41. Which of the following is a one-dimensional motion?**

- Landing of an aircraft
- Earth revolving around the sun
- Motion of wheels of a moving train
- Train running on a straight track

**Answer:** 4. Train running on a straight track

**In this type of question, more than one option are correct.**

**Question 42. A body will speed up if**

- Velocity and acceleration are in the same direction.
- Velocity and acceleration are in opposite directions.
- Velocity and acceleration are in perpendicular, directions.
- Velocity and acceleration are acting at an acute angle with respect to each other.

**Answer:**

1. Velocity and acceleration are in the same direction.

4. Velocity and acceleration are acting at an acute angle with respect to each other.

**Question 43. Two bodies having masses m _{1} and m_{2} are dropped from heights h_{1} and h_{2} respectively. They reach the ground after times t_{1} and t_{2} and strike the ground with velocities v_{1} and v_{2 }respectively, Choose the correct relations from the following:**

- \(\frac{t_1}{t_2}=\sqrt{\frac{h_1}{h_2}}\)
- \(\frac{t_1}{t_2}=\sqrt{\frac{h_2}{h_1}}\)
- \(\frac{v_1}{v_2}=\sqrt{\frac{h_1}{h_2}}\)
- \(\frac{v_1}{v_2}=\frac{h_2}{h_1}\)

**Answer:**

1. \(\frac{t_1}{t_2}=\sqrt{\frac{h_1}{h_2}}\)

3. \(\frac{v_1}{v_2}=\sqrt{\frac{h_1}{h_2}}\)

**Question 44. The variation of quantity A with quantity B, plotted describes the motion of a particle in a straight line.**

- Quantity B may represent time
- Quantity A is velocity if the motion is uniform
- Quantity A is displacement if the motion is uniform
- Quantity A is velocity if the motion is uniformly accelerated

**Answer:**

1. Quantity B may represent time

3. Quantity A is displacement if the motion is uniform

4. Quantity A is velocity if the motion is uniformly accelerated

**Question 45. Mark the correct statements.**

- Instantaneous velocity is always in the direction of motion
- Instantaneous acceleration is always in the direction of motion
- Instantaneous acceleration is always in the direction of instantaneous velocity
- Instantaneous velocity and instantaneous acceleration may be in opposite directions

**Answer:**

1. Instantaneous velocity is always in the direction of motion

4. Instantaneous velocity and instantaneous acceleration may be in opposite directions

**Question 45. Of the following situations which are possible in practice?**

- Zero velocity and non-zero acceleration
- Constant velocity and variable acceleration
- Variable velocity and constant acceleration
- Non-zero velocity and zero acceleration

**Answer:**

1. Zero velocity and non-zero acceleration

3. Variable velocity and constant acceleration

4. Non-zero velocity and zero acceleration

**Question 46. In the motion of the tip of the second hand of a clock, which of the following quantities are zero after an interval of 1 minute**?

- Displacement
- Distance Travelled
- Average speed
- Average velocity

**Answer:**

1. Displacement

4. Average velocity

**Question 47. A particle is moving with a uniform acceleration along a straight line AB. Its velocity at A and B are 2 m/s and 10 m/s respectively. Then**

- The velocity is 10 m/s at the midpoint C of AB
- The velocity is 6 m/s at an intermediate point P, for which AP: PB = 1:5
- The time taken to travel the distance AC (C is the midpoint of AB) is twice that for the distance CB
- At half-time, the particle travels one-fourth of the total distance

**Answer:**

- The velocity is 10 m/s at the midpoint C of AB
- The velocity is 6 m/s at an intermediate point P, for which AP: PB = 1:5
- The time taken to travel the distance AC (C is the midpoint of AB) is twice that for the distance CB

**Question 48. The displacement (s) of a particle depends on time (t) as s = 2at² – bt³. Then**

- The particle will come to rest after a time \(\frac{4a}{3b}\)
- The particle comes back to the starting point after a time \(\frac{2a}{b}\)
- The acceleration is zero at a time \(\frac{2a}{3b}\)
- The initial velocity is zero, but the initial acceleration is not

**Answer: **All options are correct

**Question 49. An object falls from rest through a resistive medium. The equation of its motion is \(\frac{dv}{dt}\) = α – βv. Then**

- The initial acceleration = α
- At time t, the velocity = \(\frac{\alpha}{\beta}\left(1-e^{-\beta t}\right)\)
- When the acceleration is zero, the velocity = \(\frac{a}{\beta}\)
- The constant β has the dimension of time

**Answer:**

- The initial acceleration = α
- At time t, the velocity = \(\frac{\alpha}{\beta}\left(1-e^{-\beta t}\right)\)
- When the acceleration is zero, the velocity = \(\frac{a}{\beta}\)

**Question 50. The acceleration (a) and the velocity of a particle in rectilinear motion are related as a = -√v. Then**

- If the particle comes to rest after is, its initial velocity =0.25 m/s
- If the initial velocity is v
_{0}, then after a time t, velocity = \(v_0-\sqrt{v_0} t+\frac{t^2}{4}\) - If the initial velocity is v
_{0}, then after a time t, velocity =v_{0 }– at - If the initial velocity is 1 m/s, the particle comes to rest after 2 s

**Answer:**

1. If the particle comes to rest after is, its initial velocity =0.25 m/s

2. If the initial velocity is vq, then after a time t, velocity = \(v_0-\sqrt{v_0} t+\frac{t^2}{4}\)

4. If the initial velocity is 1 m/s, the particle comes to rest after 2 s

**Question 51. A body thrown vertically upwards from a point with a velocity v _{0} rises to a maximum height and then comes back to the point. Then**

- The average velocity of downward motion is \(\frac{v_0}{2}\)
- The average speed in the flight is zero
- The time of flight is \(\frac{2 v_0}{g}\)
- The acceleration in the whole flight is not uniform

**Answer:**

1. The average velocity of downward motion is \(\frac{v_0}{2}\)

3. The time of flight is \(\frac{2 v_0}{g}\)