Acceleration and velocity–time graphs
Acceleration
is the . An object that is slowing down has a negative acceleration, or . You must recall this equation:
acceleration = change in velocity ÷ time taken, or a = Δv/t
| Quantity | Symbol | Unit |
|---|---|---|
| Acceleration | a | metres per second squared (m/s²) |
| Change in velocity | Δv | metres per second (m/s) |
| Time | t | seconds (s) |
Example: a car speeds up from 0 to 24 m/s in 8 s.
- a = Δv/t
- a = (24 − 0) ÷ 8
- a = 3 m/s²
Key terms
Using v² − u² = 2as
For uniform (constant) acceleration, this equation is on the equation sheet:
, or v² − u² = 2as
| Quantity | Symbol | Unit |
|---|---|---|
| Final velocity | v | m/s |
| Initial velocity | u | m/s |
| Acceleration | a | m/s² |
| Distance | s | metres (m) |
Example 1: a car at 10 m/s accelerates at 2 m/s² for 75 m. Find its final speed.
- v² = u² + 2as = 10² + (2 × 2 × 75)
- v² = 100 + 300 = 400
- v = √400 = 20 m/s
Example 2: a car brakes from 20 m/s to rest in 40 m.
- 0² − 20² = 2 × a × 40
- −400 = 80a
- a = −5 m/s² (a deceleration of 5 m/s²)
Velocity–time graphs
On a , velocity goes up the side and time along the bottom. The of the line is the .
- A straight line sloping up: constant acceleration. Steeper means bigger acceleration.
- A flat line: constant velocity (no acceleration).
- A line sloping down: deceleration.
Example: a line goes straight from 0 to 12 m/s in 4 s.
acceleration = gradient = 12 ÷ 4 = 3 m/s²
Area under a velocity–time graph (Higher tier only)
The area under a velocity–time graph equals the (or displacement).
Example: for the line from 0 to 12 m/s in 4 s, the area is a triangle.
- area = ½ × base × height
- area = ½ × 4 × 12
- distance = 24 m
Split more complicated shapes into triangles and rectangles. For a curved line, count the squares under it and multiply by the distance each square stands for.
Free fall and terminal velocity
An object falling freely near the Earth's surface accelerates at about 9.8 m/s².
An object falling through a , such as a skydiver through air:
- At first, it accelerates because its weight is the only big force.
- As it speeds up, increases, so the resultant force and acceleration get smaller.
- Eventually air resistance equals its weight. The resultant force is zero, so it falls at a steady speed: its .
When the skydiver opens a parachute, air resistance increases suddenly, so they slow down to a new, lower terminal velocity.
On a velocity–time graph, the line curves up steeply at first, then levels off to a flat line.