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Motion in a Straight Line
Physics · Class 11NCERT pp. 13–212 sets × 25 questionsFree
Key facts and formulas for Motion in a Straight Line, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Velocity and acceleration | v = dx/dt, a = dv/dt = v dv/dx. Slope of x–t is v, slope of v–t is a |
| Area under graphs | Area under v–t = displacement. Area under a–t = change in velocity |
| Equations for constant a | v = v₀ + at, x = v₀t + ½at², v² = v₀² + 2ax, x = ½(v + v₀)t |
| Distance in nth second | S_n = u + a(n − ½). For free fall from rest, S_n = (g/2)(2n − 1) |
| Average speed | Total distance / total time. Equal distances: 2v₁v₂/(v₁ + v₂). Equal times: (v₁ + v₂)/2 |
| Distance vs displacement | Distance ≥ |displacement|. A round trip has zero displacement |
| Free fall and projection | Time to top = u/g, H = u²/2g, T = 2u/g. Return speed equals projection speed |
| Stopping distance | d = u²/2a, so d ∝ u². Check the stopping time u/a before using a given time |
| Relative motion | Opposite directions: speeds add. Same direction: speeds subtract. Equal a means relative a = 0 |
| Unit conversion | km/h to m/s: divide by 3.6. Convert cm to m before using g = 10 m/s² |
Three sample questions
Q1. In which case is the 'point object' idea NOT valid?
- A ship sailing across the ocean
- A 100 m long train crossing a 200 m long bridge
- A car going 400 km between two cities
- A satellite orbiting the Earth, seen from far away
Hint and solution
Hint: A body can be treated as a point only if its size is very small compared with the distance it moves. Check which option fails this.
- Point object: size << distance moved — A body is a point object only when its size is much smaller than the distance it covers.
- Ship, car, satellite: size << distance — In the ship, car and satellite cases, the size is tiny against thousands of metres or kilometres.
- Train 100 m vs bridge 200 m — The train is 100 m long and moves just 200 m. The two are comparable, so the length matters.
- So the point idea fails for the train — The point object idea is not valid for the train on the bridge. Option B.
Answer: B. The train's length (100 m) is comparable with the distance moved (200 m), so its size matters.
Q2. Statement I: Kinematics studies motion without considering its cause. Statement II: The cause of motion, force, is studied in dynamics.
- Statement I is true, Statement II is false
- Statement I is false, Statement II is true
- Both statements are false
- Both statements are true
Hint and solution
Hint: Recall what kinematics and dynamics each deal with. One describes motion, the other explains why it happens.
- Kinematics = how things move — Kinematics describes position, velocity and acceleration without asking what causes them.
- Dynamics = why things move — Dynamics studies the cause of motion, which is force.
- Check both statements — Statement I matches the definition of kinematics. Statement II matches the definition of dynamics.
- Both true — Since both are correct, the answer is that both statements are true. Option D.
Answer: D. Both are exactly how the two branches are defined.
Q3. The position of a particle is x = 3t² + 2t (x in m, t in s). Its velocity at t = 2 s is
- 14 m/s
- 12 m/s
- 16 m/s
- 10 m/s
Hint and solution
Hint: Velocity is the rate of change of position, so differentiate x with respect to t, then put t = 2.
- v = dx/dt — Velocity is the derivative of position with respect to time.
- dx/dt = 6t + 2 — Differentiate 3t² to get 6t and 2t to get 2.
- t = 2: v = 6 × 2 + 2 = 14 — Put t = 2 s: six times two is twelve, plus two is fourteen metres per second.
- v = 14 m/s — So the velocity at 2 seconds is 14 metres per second. Option A.
Answer: A. v = dx/dt = 6t + 2. At t = 2 s, v = 14 m/s.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.