Velocity-time graphs
If an object moves along a straight line, its motion can be represented by a velocity-time graph. The gradient of the line is equal to the acceleration of the object.
The table shows what each section of the graph represents:
| Section of graph | Gradient | Velocity | Acceleration |
| A | postive | increasing | postive |
| B | zero | constant | zero |
| C | negative | decreasing | negative |
| D | zero | stationary (at rest) | zero |
| Section of graph | A |
|---|---|
| Gradient | postive |
| Velocity | increasing |
| Acceleration | postive |
| Section of graph | B |
|---|---|
| Gradient | zero |
| Velocity | constant |
| Acceleration | zero |
| Section of graph | C |
|---|---|
| Gradient | negative |
| Velocity | decreasing |
| Acceleration | negative |
| Section of graph | D |
|---|---|
| Gradient | zero |
| Velocity | stationary (at rest) |
| Acceleration | zero |
Example
Describe the motion of the vehicle in the graph at the three stages of its journey.
Between 0 s and 4 s the vehicle is accelerating.
\(acceleration = \frac{change~in~velocity}{time~taken}\)
This means that: \(8 \div 2 = 4 m/s^2\)
Between 4 s and 7 s the vehicle has a constant velocity of 8 m/s.
Between 7 s and 10 s, the vehicle is decelerating so: \(-8 \div 3 = -2.67~m/s^2\)
Calculating displacement - Higher
The Quantity describing the distance from the start of the journey to the end in a straight line with a described direction, eg 50 km due north of the original position. of an object can be calculated from the area under a velocity-time graph.
The area under the graph can be calculated by:
- using geometry (if the lines are straight)
- counting the squares beneath the line (particularly if the lines are curved)
Example
Calculate the total displacement of the object whose motion is represented by the velocity-time graph below.
The displacement can be found by calculating the total area of the shaded sections below the line.
Find the area of the triangle:
\(\frac{1}{2} \times base \times height\)
\(\frac{1}{2} \times 4 \times 8 = 16~m^{2}\)
Find the area of the rectangle:
base 脳 height
(10 - 4) 脳 8 = 48 m2
Add the areas together to find the total displacement:
(16 + 48) = 64 m