Equations of motion
Section: Kinematics | Syllabus: Cambridge AS Level Physics (9702)
Motion Graphs
Graphs are powerful tools for visualizing motion. You need to be able to interpret the gradient and the area under these graphs.
1. Displacement-Time (s-t) Graphs
- Gradient = Velocity
- A straight line (constant gradient) indicates constant velocity.
- A horizontal line (zero gradient) indicates the object is stationary.
- A curve (changing gradient) indicates acceleration or deceleration.
2. Velocity-Time (v-t) Graphs
- Gradient = Acceleration
- Area under the graph = Displacement
- A straight line indicates uniform (constant) acceleration.
- A horizontal line indicates constant velocity (zero acceleration).
To find the velocity at a specific point on a curved displacement-time graph, draw a tangent to the curve at that point and calculate its gradient.
The Equations of Motion (SUVAT)
For an object moving with uniform (constant) acceleration in a straight line, we use the five equations of motion. The variables are:
- s = Displacement
- u = Initial velocity
- v = Final velocity
- a = Acceleration
- t = Time taken
1. v = u + at (derived from a = (v-u/t))
2. s = (1/2)(u + v)t (average velocity × time)
3. s = ut + (1/2)at^2
4. v^2 = u^2 + 2as
Worked Example: Stopping DistanceQuestion: A car traveling at 20 m s^-1 decelerates uniformly to rest in 4.0 s. Calculate the distance traveled during this time.
SolutionIdentify knowns: u = 20, v = 0, t = 4.0, find s.
Choose equation: s = (1/2)(u + v)t
s = (1/2)(20 + 0) × 4.0 s = 10 × 4.0 = 40 mInteractive revision notes, videos and practice questions load below.