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Motion in a Straight Line is the first real chapter of JEE Main physics, and it sets the habit for everything after it. The three equations of motion will carry you only so far — the paper will also hand you a position written as a function of time and expect you to differentiate it, or a velocity and expect you to integrate. Get comfortable with both routes now. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 1 to 2 questions every year, which is 4 to 8 marks.
- Calculus-based kinematics and graph reading are the regular ones.
- Free fall and relative motion fill the rest.
What the syllabus says
In the syllabus (Unit 2, Kinematics): Frame of reference, motion in a straight line, speed and velocity, uniform and non-uniform motion, average speed and instantaneous velocity, uniformly accelerated motion, velocity–time and position–time graphs, relations for uniformly accelerated motion, relative velocity.
Taken out in 2024: the vector block — scalars and vectors, addition and subtraction, zero vector, scalar and vector products, unit vector, resolution of a vector.
Taken from the NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| First equation | v = u + at |
| Second equation | s = ut + ½at2 |
| Third equation | v2 = u2 + 2as |
| Distance in the nth second | sn = u + a(2n − 1)/2 |
| By calculus | v = dx/dt, a = dv/dt = v dv/dx |
| Displacement from velocity | s = ∫ v dt |
| Slope of a graph | x–t gives velocity, v–t gives acceleration |
| Area under a graph | v–t gives displacement, a–t gives change in velocity |
| Free fall | h = ½gt2, t = √(2h/g) |
| Vertical throw | time of flight T = 2u/g |
Note the third form of acceleration, a = v dv/dx. When a question gives you acceleration as a function of position rather than time, that is the form that works, and the three standard equations will not help you at all.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. The position of a particle is x = 4t3 − 2t metre. Its acceleration at t = 1 s is
- (a) 10 m/s2
- (b) 24 m/s2
- (c) 12 m/s2
- (d) 22 m/s2
Q2. A body starts from rest with uniform acceleration. The distances covered in the first, second and third seconds are in the ratio
- (a) 1 : 2 : 3
- (b) 1 : 3 : 5
- (c) 1 : 4 : 9
- (d) 1 : 1 : 1
Q3. A car moving at 20 m/s is brought to rest uniformly in 4 s. The distance it covers is
- (a) 20 m
- (b) 40 m
- (c) 80 m
- (d) 10 m
Q4. A ball is thrown vertically upward with 20 m/s. Taking g = 10 m/s2, its total time of flight is
- (a) 2 s
- (b) 4 s
- (c) 1 s
- (d) 8 s
Q5. The area under an acceleration–time graph gives the
- (a) displacement
- (b) change in velocity
- (c) distance travelled
- (d) rate of change of acceleration
Q6. A particle moves with velocity v = 3t2 m/s. Its displacement between t = 0 and t = 2 s is
- (a) 4 m
- (b) 8 m
- (c) 12 m
- (d) 6 m
Q7. Two bodies are dropped from heights h and 4h. The ratio of their times of fall is
- (a) 1 : 2
- (b) 1 : 4
- (c) 2 : 1
- (d) 1 : 16
Q8. A body moving with constant speed along a straight line has an acceleration that is
- (a) constant and non-zero
- (b) zero
- (c) steadily increasing
- (d) equal to g
Q9. A train slows uniformly from 30 m/s to 10 m/s over a distance of 100 m. Its retardation is
- (a) 2 m/s2
- (b) 4 m/s2
- (c) 8 m/s2
- (d) 1 m/s2
Q10. The displacement of a particle is zero while the distance it travelled is not. This happens when the particle
- (a) moves along a straight line
- (b) comes back to its starting point
- (c) stays at rest
- (d) never, it is impossible
Answer key, with a hint for each
| Q1 | (b) | v = 12t2 − 2 and a = 24t, so a = 24 at t = 1. |
| Q2 | (b) | From sn = a(2n − 1)/2 with u = 0. The odd numbers 1, 3, 5 come straight out of it. |
| Q3 | (b) | Average velocity is 10 m/s for 4 s. Or use v2 = u2 + 2as. |
| Q4 | (b) | T = 2u/g = 40/10. Half of it going up, half coming down. |
| Q5 | (b) | Acceleration times time is a change in velocity, and that product is exactly what the area adds up. |
| Q6 | (b) | s = ∫02 3t2 dt = [t3] from 0 to 2. |
| Q7 | (a) | t ∝ √h, so √1 : √4. |
| Q8 | (b) | Constant speed in a straight line means neither the size nor the direction of the velocity changes. |
| Q9 | (b) | v2 = u2 + 2as gives 100 = 900 + 200a, so a = −4 m/s2. |
| Q10 | (b) | Displacement counts only where you started and where you ended. Distance counts every metre of the path. |
Now mark yourself honestly
JEE Main marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 25 Physics questions are out of 100.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in January.
The full chapter, on a clock
Ten questions tell you a little. Twenty-five tell you the truth.
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