Chapter 2: Motion in a Straight Line
Original notes — ready CBSE (NCERT, English Medium) • Class 11 • Physics • Book: Physics — Part I
Motion in a Straight Line — EG's own summary, in simple words
Book: Physics — Part I (CBSE, Class 11) | Chapter 2 | Medium: English
Motion in a straight line is the simplest motion to study — a car on a straight road, a ball dropped from a height, a train on a straight track. Everything here moves along one line, so we can describe it with just one direction: forward or backward, up or down.
Diagram (labels on the image): Motion in a straight line: the car starts at the flag and passes distance posts. Distance counts every metre travelled; displacement counts only the change from the start.
1. Position, distance and displacement
Position tells us where an object is, measured from a fixed origin. Distance is the total path actually travelled — it is always positive and it grows as the object moves. Displacement is the change in position: final position minus initial position. Displacement can be positive, negative or zero, and it is often smaller than the distance. Example: if you walk 3 m east and then 3 m back west, your distance is 6 m but your displacement is zero, because you are back where you started.
2. Speed and velocity
Speed is distance divided by time — how fast, without saying which way. Velocity is displacement divided by time — how fast, and in which direction. Average speed is total distance over total time, while average velocity is total displacement over total time. Instantaneous velocity is the velocity at one single moment, which is what a speedometer shows. A car can have a high average speed but zero average velocity if it returns to its starting point.
3. Acceleration
Acceleration is the rate of change of velocity — how quickly velocity changes. If velocity increases, acceleration is positive; if it decreases, acceleration is negative (sometimes called retardation). Uniform acceleration means velocity changes by equal amounts in equal times. Free fall is the classic example: a falling body accelerates downwards at about 9.8 m/s² (g) if air resistance is ignored. Zero acceleration does not mean zero velocity — a car cruising steadily at 60 km/h has velocity but no acceleration.
4. Equations of uniformly accelerated motion
When acceleration is constant, three equations connect the quantities: v = u + at, s = ut + ½at², and v² = u² + 2as, where u is initial velocity, v is final velocity, a is acceleration, t is time and s is displacement. The first comes from the definition of acceleration, the second from average velocity over time, and the third by combining the two. The trick in problems is to list what is given, what is asked, and pick the equation that contains exactly those quantities.
5. Reading motion graphs
A position-time graph shows where an object is at each moment: its slope is velocity. A straight, sloping line means constant velocity; a horizontal line means the object is at rest. A velocity-time graph is even more useful: its slope is acceleration, and the area under the graph is displacement. A straight line sloping up on a velocity-time graph means uniform acceleration. Learning to read these two graphs is worth more than memorising formulas, because most graph questions test slope and area.
Chart / Table — Equations of uniformly accelerated motion — when to use each
| Equation | Use it when you know | You do NOT need |
|---|---|---|
| v = u + at | u, a, t | s |
| s = ut + ½at² | u, a, t | v |
| v² = u² + 2as | u, a, s | t |
Caption: A sprinter on a straight track — the simplest motion: one line, one direction, and speed, velocity and acceleration all measured along it.
Practice set — try it yourself
- A boy walks 4 m east, then 3 m west. Find his distance and his displacement. Hint: Distance adds up; displacement is final position minus starting position.
- A car travels 60 km in 2 hours and returns the same 60 km in 3 hours. Find its average speed and its average velocity for the whole trip. Hint: Average speed uses total distance; average velocity uses total displacement.
- A ball is dropped from rest. How fast is it moving after 3 s? Take g = 10 m/s². Hint: Use v = u + at with u = 0.
- A train moving at 20 m/s brakes with uniform retardation of 2 m/s². How far does it travel before stopping? Hint: Final velocity is zero; pick the equation without t.
- On a velocity-time graph, what do the slope and the area under the graph give? Hint: Think: velocity changing gives one quantity; velocity × time gives another.
Key Terms / Important Terms
- Position — where an object is, measured from a fixed origin.
- Distance — total path length travelled; always positive.
- Displacement — change in position (final minus initial); can be negative or zero.
- Speed — distance ÷ time; no direction.
- Velocity — displacement ÷ time; has direction.
- Average velocity — total displacement ÷ total time.
- Instantaneous velocity — velocity at one particular instant.
- Acceleration — rate of change of velocity.
- Uniform acceleration — velocity changing by equal amounts in equal times.
- Free fall — motion under gravity alone, with acceleration g ≈ 9.8 m/s² downwards.
Remember
- Distance is total path; displacement is straight change in position — they are equal only for straight motion in one direction.
- Slope of a position-time graph = velocity; slope of a velocity-time graph = acceleration; area under velocity-time graph = displacement.
- Constant velocity means zero acceleration, not zero motion.
- In free fall, take g = 9.8 m/s² downwards and be careful with signs.
- List given, wanted and the missing quantity before choosing an equation.
Exam Tip / Common Mistake
Common mistake: using distance and displacement as if they were the same. In a return journey the distance keeps growing but the displacement can fall back to zero, so average speed and average velocity give different answers. Read the question: if it says 'how far', it may mean distance; if it says 'how far from the start', it means displacement.
Questions with Answers — full answers
- Distinguish between distance and displacement with an example. Answer: Distance is the total path travelled and is always positive. Displacement is the change in position and can be zero or negative. Walking 4 m east and 4 m back west gives distance 8 m but displacement zero.
- A car moves at a constant speed of 50 km/h on a straight road. What is its acceleration? Explain. Answer: Zero. Acceleration is the rate of change of velocity, and the velocity is not changing, so acceleration is zero even though the car is moving.
- A stone is thrown upwards at 20 m/s. How high does it go? Take g = 10 m/s². Answer: At the top, v = 0. Using v² = u² + 2as with a = −10 m/s²: 0 = 400 − 20s, so s = 20 m.
- Why is the area under a velocity-time graph equal to displacement? Answer: Area = velocity × time, and velocity × time is displacement (distance in a direction). For changing velocity, the area still adds up all the small velocity × time pieces, giving total displacement.
- A body starts from rest and moves with uniform acceleration 2 m/s² for 5 s. Find its final velocity and displacement. Answer: v = u + at = 0 + 2 × 5 = 10 m/s. s = ut + ½at² = 0 + ½ × 2 × 25 = 25 m.