Motion in a Straight Line

28 NEET-UG practice questions on Motion in a Straight Line, part of Physics. The first 25 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
The position of a particle is x = 2t³ − 9t² + 12t + 1, with x in metres and t in seconds. What is its acceleration at the instant its velocity becomes zero for the second time?
1. A+6 m/s²
2. BZero
3. C−6 m/s²
4. D+24 m/s²
Show answerHide answer
Answer: A · +6 m/s²
v = dx/dt = 6t² − 18t + 12 = 6(t − 1)(t − 2), so v = 0 at t = 1 s and t = 2 s. a = dv/dt = 12t − 18, and at t = 2 s this is +6 m/s².
- B: This assumes acceleration vanishes when velocity does.
- C: This is the acceleration at the first stop, t = 1 s.
- D: This leaves out the −18 term of the acceleration.
Remember this
Zero velocity does not mean zero acceleration; differentiate first, then substitute the time.
Question 2 · Easy
Match List-I with List-II. List-I (feature of a graph) A. Slope of the x-t graph B. Slope of the v-t graph C. Area under the v-t graph D. Area under the a-t graph List-II (what it gives) I. Displacement II. Change in velocity III. Velocity IV. Acceleration
1. AA-III, B-IV, C-I, D-II
2. BA-III, B-IV, C-II, D-I
3. CA-IV, B-III, C-I, D-II
4. DA-I, B-IV, C-III, D-II
Show answerHide answer
Answer: A · A-III, B-IV, C-I, D-II
Velocity is dx/dt and acceleration is dv/dt, so these are slopes. Displacement is the integral of v dt and change in velocity is the integral of a dt, so these are areas.
- B: This swaps the two areas.
- C: This swaps the two slopes.
- D: This swaps the slope of the x-t graph with the area under the v-t graph.
Remember this
Slope differentiates and area integrates, moving one step along x, v, a.
Question 3 · Hard
A particle starts from rest and moves along a line with acceleration a = (6 − 2t) m/s², t in seconds. How far has it travelled when it next comes to rest?
1. A27 m
2. B36 m
3. C108 m
4. D72 m
Show answerHide answer
Answer: B · 36 m
v = 6t − t², which is zero again at t = 6 s, and v stays positive in between. x = 3t² − t³/3 = 108 − 72 = 36 m. Check: the v-t curve is a parabola with peak 9 m/s, and its area is (2/3)(9)(6) = 36 m.
- A: This treats the curved v-t graph as a triangle.
- C: This keeps only the 3t² term of the displacement.
- D: This keeps only the t³/3 term of the displacement.
Remember this
With time-dependent acceleration, integrate twice; the constant-acceleration equations do not apply.
Question 4 · Medium
Starting from rest, a lift's speed rises uniformly to 4 m/s in 2 s. The lift then runs at this speed for 5 s and slows uniformly to rest in another 3 s, all in one direction. What is its average velocity for the whole trip?
1. A3 m/s
2. B4 m/s
3. C2 m/s
4. D2.67 m/s
Show answerHide answer
Answer: A · 3 m/s
Displacement is the area of the v-t trapezium: 4 + 20 + 6 = 30 m. Check: (1/2)(5 + 10)(4) = 30 m. Average velocity = 30/10 = 3 m/s.
- B: This is the peak speed, not the average.
- C: This is the average during the speeding-up stage alone.
- D: This takes the mean of the three stage averages without weighting by time.
Remember this
Average velocity = total displacement/total time, never the mean of the speeds in the separate stages.
Question 5 · Medium
A ball is thrown straight up from the ground at 30 m/s. At the same instant, a second ball is released from rest at a point 60 m directly above the first. Taking g = 10 m/s², at what height above the ground do they meet?
1. A40 m
2. B60 m
3. C20 m
4. D30 m
Show answerHide answer
Answer: A · 40 m
Both balls have the same acceleration, so their relative speed stays 30 m/s and they meet at t = 60/30 = 2 s. Height of the first ball = 30 × 2 − 5 × 4 = 40 m. Check: the dropped ball falls 5 × 4 = 20 m, and 60 − 20 = 40 m.
- B: This is the starting height of the dropped ball.
- C: This is how far the dropped ball falls, not the meeting height.
- D: This assumes they meet halfway.
Remember this
Two bodies in free fall have zero relative acceleration, so their relative velocity stays constant.
Question 6 · Hard
Starting from rest at the origin, a particle moves along a line with the acceleration-time graph shown. How far is it from the origin at the instant its speed is greatest?
Figure: MedExams
1. A13.5 m
2. B18 m
3. C27 m
4. D9 m
Answer and explanation in LearnFree account
Question 7 · Medium
Position of a runner on a straight road is plotted against time, with +x as the positive direction. Over the full 10 s, what are the average speed and the average velocity?
Figure: MedExams
1. A6.25 m/s and −1 m/s
2. B1 m/s and −1 m/s
3. C5 m/s and −1 m/s
4. D5 m/s and +1 m/s
Answer and explanation in LearnFree account
Question 8 · Easy
A cart moves along a straight track without reversing. Using its velocity-time graph, find the distance it covers in the 8 s shown.
Figure: MedExams
1. A54 m
2. B66 m
3. C96 m
4. D48 m
Answer and explanation in LearnFree account
Question 9 · Medium
From rest, a scooter on a straight road has acceleration +2 m/s² for the first 2 s, zero for the next 2 s and −2 m/s² for the last 2 s. Its velocity against time is correctly shown by which graph?
Figure: MedExams
1. AGraph B
2. BGraph D
3. CGraph A
4. DGraph C
Answer and explanation in LearnFree account
Question 10 · Hard
When a car moving at 20 m/s is to be stopped, the driver needs 0.5 s to react before braking starts, and the car then travels a total of 30 m from the moment the driver sees the danger. With the same reaction time and the same braking deceleration, what total distance does it travel before stopping from 30 m/s?
1. A60 m
2. B45 m
3. C67.5 m
4. D55 m
Answer and explanation in LearnFree account
Question 11 · Medium
Along the x-axis, a particle starts from rest at the origin at t = 0. Its acceleration is given by a = 6t, with a in m/s² and t in s. Where is it at t = 2 s?
1. Ax = 12 m
2. Bx = 8 m
3. Cx = 4 m
4. Dx = 24 m
Answer and explanation in LearnFree account
Question 12 · Medium
On a straight highway, a motorcycle of negligible length moving at 25 m/s comes up behind a truck 120 m long moving at 15 m/s in the same direction. How long does the motorcycle take to go from the rear end of the truck to its front end?
1. A4.8 s
2. B3 s
3. C12 s
4. D8 s
Answer and explanation in LearnFree account
Question 13 · Medium
For a body moving along a straight line, the velocity is related to the position by v = 4√x, where x is in m and v in m/s. What can be said about its acceleration?
1. AIt increases as x increases
2. BIt is constant, 8 m/s²
3. CIt is constant, 4 m/s²
4. DIt is constant, 16 m/s²
Answer and explanation in LearnFree account
Question 14 · Easy
A car pulls away from a traffic light along a straight road with steady acceleration. Which curve describes its position-time (x-t) graph?
1. AA straight line through the origin
2. BA hyperbola
3. CA straight line parallel to the time axis
4. DA parabola
Answer and explanation in LearnFree account
Question 15 · Medium
A ball thrown vertically upward passes a window ledge on its way up at t = 1 s and passes it again on its way down at t = 3 s after the throw. Taking g = 10 m/s² and ignoring air resistance, what was its speed of projection?
1. A20 m/s
2. B15 m/s
3. C40 m/s
4. D10 m/s
Answer and explanation in LearnFree account
Question 16 · Easy
The position-time graph of a particle moving along the x-axis is drawn here. What is its velocity at t = 3 s?
Figure: MedExams
1. A5.7 m/s
2. B4 m/s
3. C1 m/s
4. D5 m/s
Answer and explanation in LearnFree account
Question 17 · Hard
Cars P and Q move in the same direction along a straight road and are side by side at t = 0. Their velocity-time graphs for the first 6 s are drawn. What is the greatest distance between them during the 6 s shown?
Figure: MedExams
1. A40 m
2. B20 m
3. C30 m
4. D10 m
Answer and explanation in LearnFree account
Question 18 · Medium
A car moving with speed u along a straight road brakes with a constant retardation and stops after covering a distance s₀. Which graph correctly shows its velocity v against the distance s covered during braking?
Figure: MedExams
1. AGraph A
2. BGraph B
3. CGraph C
4. DGraph D
Answer and explanation in LearnFree account
Question 19 · Medium
Given below are two statements: Statement I: For a body moving with uniform velocity, the position-time graph is a straight line inclined to the time axis. Statement II: For a body moving with uniform acceleration, the velocity-time graph is a parabola. Choose the correct answer.
1. AStatement I is correct but Statement II is incorrect
2. BBoth Statement I and Statement II are incorrect
3. CStatement I is incorrect but Statement II is correct
4. DBoth Statement I and Statement II are correct
Answer and explanation in LearnFree account
Question 20 · Easy
A body starts from rest and moves with uniform acceleration. In what ratio are the distances it covers in the first, second and third seconds?
1. A1 : 4 : 9
2. B1 : 3 : 5
3. C1 : 2 : 3
4. D1 : 1 : 1
Answer and explanation in LearnFree account
Question 21 · Easy
A stone dropped from rest from the top of a cliff reaches the ground in 3 s. Taking g = 10 m/s² and ignoring air resistance, how high is the cliff?
1. A25 m
2. B90 m
3. C30 m
4. D45 m
Answer and explanation in LearnFree account
Question 22 · Hard
The velocity of a particle moving along the x-axis is v = (3t² − 12) m/s, with t in seconds. What distance does it travel between t = 0 and t = 3 s?
1. A9 m
2. B16 m
3. C23 m
4. D25 m
Answer and explanation in LearnFree account
Question 23 · Hard
A body falls freely from rest and covers 9/25 of the total height in the last second of its fall. Taking g = 10 m/s², from what height did it fall?
1. A125 m
2. B180 m
3. C245 m
4. D80 m
Answer and explanation in LearnFree account
Question 24 · Medium
A particle starts from rest at t = 0 and its acceleration varies with time as a = 4t (a in m/s², t in s). What distance does it cover in the first 3 s?
1. A36 m
2. B27 m
3. C54 m
4. D18 m
Answer and explanation in LearnFree account
Question 25 · Easy
A ball is thrown vertically upward. Ignoring air resistance, what is true at its highest point?
1. AVelocity zero; acceleration g, upward
2. BVelocity zero; acceleration zero
3. CVelocity maximum; acceleration zero
4. DVelocity zero; acceleration g, downward
Answer and explanation in LearnFree account

3 more Motion in a Straight Line questions

Answer them one by one, keep your score and see your weak topics in Learn. Signed-out visitors try 25 per exam; sign in with Google to see them all.

Study Physics

Motion in a Straight Line

The position of a particle is x = 2t³ − 9t² + 12t + 1, with x in metres and t in seconds. What is its acceleration at the instant its velocity becomes zero for the second time?

Match List-I with List-II. List-I (feature of a graph) A. Slope of the x-t graph B. Slope of the v-t graph C. Area under the v-t graph D. Area under the a-t graph List-II (what it gives) I. Displacement II. Change in velocity III. Velocity IV. Acceleration

A particle starts from rest and moves along a line with acceleration a = (6 − 2t) m/s², t in seconds. How far has it travelled when it next comes to rest?

Starting from rest, a lift's speed rises uniformly to 4 m/s in 2 s. The lift then runs at this speed for 5 s and slows uniformly to rest in another 3 s, all in one direction. What is its average velocity for the whole trip?

A ball is thrown straight up from the ground at 30 m/s. At the same instant, a second ball is released from rest at a point 60 m directly above the first. Taking g = 10 m/s², at what height above the ground do they meet?

Starting from rest at the origin, a particle moves along a line with the acceleration-time graph shown. How far is it from the origin at the instant its speed is greatest?

Position of a runner on a straight road is plotted against time, with +x as the positive direction. Over the full 10 s, what are the average speed and the average velocity?

A cart moves along a straight track without reversing. Using its velocity-time graph, find the distance it covers in the 8 s shown.

From rest, a scooter on a straight road has acceleration +2 m/s² for the first 2 s, zero for the next 2 s and −2 m/s² for the last 2 s. Its velocity against time is correctly shown by which graph?

Along the x-axis, a particle starts from rest at the origin at t = 0. Its acceleration is given by a = 6t, with a in m/s² and t in s. Where is it at t = 2 s?

On a straight highway, a motorcycle of negligible length moving at 25 m/s comes up behind a truck 120 m long moving at 15 m/s in the same direction. How long does the motorcycle take to go from the rear end of the truck to its front end?

For a body moving along a straight line, the velocity is related to the position by v = 4√x, where x is in m and v in m/s. What can be said about its acceleration?

A car pulls away from a traffic light along a straight road with steady acceleration. Which curve describes its position-time (x-t) graph?

A ball thrown vertically upward passes a window ledge on its way up at t = 1 s and passes it again on its way down at t = 3 s after the throw. Taking g = 10 m/s² and ignoring air resistance, what was its speed of projection?

The position-time graph of a particle moving along the x-axis is drawn here. What is its velocity at t = 3 s?

Cars P and Q move in the same direction along a straight road and are side by side at t = 0. Their velocity-time graphs for the first 6 s are drawn. What is the greatest distance between them during the 6 s shown?

A car moving with speed u along a straight road brakes with a constant retardation and stops after covering a distance s₀. Which graph correctly shows its velocity v against the distance s covered during braking?

Given below are two statements: Statement I: For a body moving with uniform velocity, the position-time graph is a straight line inclined to the time axis. Statement II: For a body moving with uniform acceleration, the velocity-time graph is a parabola. Choose the correct answer.

A body starts from rest and moves with uniform acceleration. In what ratio are the distances it covers in the first, second and third seconds?

A stone dropped from rest from the top of a cliff reaches the ground in 3 s. Taking g = 10 m/s² and ignoring air resistance, how high is the cliff?

The velocity of a particle moving along the x-axis is v = (3t² − 12) m/s, with t in seconds. What distance does it travel between t = 0 and t = 3 s?

A body falls freely from rest and covers 9/25 of the total height in the last second of its fall. Taking g = 10 m/s², from what height did it fall?

A particle starts from rest at t = 0 and its acceleration varies with time as a = 4t (a in m/s², t in s). What distance does it cover in the first 3 s?

A ball is thrown vertically upward. Ignoring air resistance, what is true at its highest point?