Q1. A train accelerates from 10 m/s to 30 m/s over a distance of 400 m. Find its acceleration.
v² = u² + 2as
30² = 10² + 2a(400)
900 − 100 = 800a ⇒ a = 800/800 = 1 m/s²
Motion in a Straight Line — Class 11
One-dimensional motion is all about three equations. Compute velocity and displacement for any u, a and t, then drill the numericals.
Displacement & velocityDisplacement is the change in position (a vector). Average velocity = displacement/time; instantaneous velocity is its limit as t→0.
AccelerationThe rate of change of velocity, a = dv/dt. Uniform acceleration means a is constant.
Equations of motionFor uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
Motion graphsSlope of a position–time graph = velocity; slope of a velocity–time graph = acceleration; area under v–t = displacement.
Kinematics calculator Interactive
Enter initial velocity, acceleration and time to get the final velocity and displacement.
Final velocity, v = u+at—m/s
Displacement, ut+½at²—m
Try a negative acceleration (retardation) — the object slows down and can even reverse.
Numericals practice Interactive
Kinematics problems with full steps.
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Solved numericals
Q2. A stone thrown up at 20 m/s. How high does it rise? (g = 10 m/s²)
At the top v = 0; a = −g = −10
v² = u² + 2as ⇒ 0 = 400 − 20s
s = 400/20 = 20 m
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| First equation | v = u + a t | m/s |
| Second equation | s = u t + ½ a t² | m |
| Third equation | v² = u² + 2 a s | — |
| Average velocity | (u + v) / 2 | m/s |
Common mistakes & exam wins
- Choose a positive direction first; deceleration is just negative acceleration.
- "Starts from rest" ⇒ u = 0; "comes to rest" ⇒ v = 0.
- Use v² = u² + 2as when time is not given.
- Area under a velocity–time graph gives the displacement.
Frequently asked questions
What are the three equations of motion?
For uniform acceleration: v = u + at, s = ut + ½at², and v² = u² + 2as.
What is the difference between distance and displacement?
Distance is the total path length (scalar); displacement is the straight-line change in position with direction (vector).
What does the slope of a velocity–time graph represent?
The acceleration of the object; the area under the graph gives the displacement.