Mechanics
Motion Graphs and SUVAT
Pearson Edexcel International A Level Physics
Equations of uniform acceleration
displacement = average velocity × times = (u + v)t / 2
final velocity = initial velocity + acceleration × timev = u + a t
uniform accelerations = u t + ½ a t2
uniform accelerationv2 = u2 + 2 a s
- These equations hold only for uniform acceleration.
- Free fall means weight is the only force acting on the object: its acceleration is g.
Method: using the equations of motion
- Choose one direction as positive and keep every sign consistent: with up positive, a = −g, and a displacement below the starting point is negative.
- List the three known quantities and the one wanted, then choose the equation that links them.
Motion graphs
- Velocity is the rate of change of displacement; acceleration is the rate of change of velocity.
- Average speed = total distance / total time; average velocity = total displacement / total time. Uniform acceleration from rest, or to rest: the average speed is half the greatest speed.
| Graph | Gradient | Area under graph |
|---|---|---|
| Displacement-time | velocity | no meaning |
| Velocity-time | acceleration | displacement |
| Acceleration-time | no meaning | change in velocity |
Method: gradient of a curved graph at an instant
- Draw a tangent at the instant: a straight line that touches the curve there.
- Read values for Δv and Δt from the tangent: gradient = Δv / Δt.
- On a velocity-time graph the gradient is the acceleration; on a displacement-time graph it is the velocity.
- A curving displacement-time graph means the velocity is changing.
- Starting from rest: the tangent is horizontal at t = 0, as the initial gradient = 0.
- Area below the time axis is a negative displacement: the object is back at its start when the area above the axis equals the area below it.
Falling to terminal velocity
- Displacement-time graph: initially the velocity is zero so gradient is zero; the gradient increases until terminal velocity when the gradient becomes constant.
- Velocity-time graph, with up positive: a curved line starting at zero with negative gradient decreasing in magnitude, then a horizontal line once terminal velocity is reached.
Bouncing ball
- When the ball is in the air it always has a constant downward acceleration, g: a horizontal line on an acceleration-time graph.
- The velocity is zero when the ball reaches the maximum height.
Core practical 1
Core practical 1: Determine the acceleration of a freely-falling object
- An electromagnet holds a steel ball above a trapdoor. The switch and the trapdoor are connected to an electronic timer.
- Measure the height s from the bottom of the ball to the trapdoor with a metre rule.
- Open the switch: the timer starts and the ball falls from rest, so u = 0.
- The ball hits the trapdoor and the timer stops: record the time t. Electronic timing eliminates human reaction time.
- Repeat and calculate an average time at each height.
- Repeat for different heights.
- Plot s against t2, with time in s and distance in m.
- From s = ut + ½at2 with u = 0, s is proportional to t2 so the gradient of graph is constant: a straight line through origin.
- The gradient is g / 2, so g = 2 × gradient.
- With a light gate: a rod falls through the gate and v = length of rod / time to pass through the light gate.
- Repeat at different release heights and plot v2 against s: the gradient is 2g.
Quantities and units
| Quantity | Symbol | Unit |
|---|---|---|
| Displacement | s | m |
| Initial velocity | u | m s−1 |
| Final velocity | v | m s−1 |
| Acceleration | a | m s−2 |
| Time | t | s |
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