- Displacement-time graphs show the changing position of an object in motion
- They also show whether an object is moving forwards (positive displacement) or backwards (negative displacement)
Velocity = Gradient of a displacement-time graph
- The greater the slope, the greater the velocity
- A negative gradient = a negative velocity (the object is moving backwards)
A car driver sees a hazard ahead and applies the brakes to bring the car to rest.
What does the displacement-time graph look like?
- Velocity-time graphs show the speed and direction of an object in motion over a specific period of time
- The area under a velocity-time graph is equal to the displacement of a moving object
Displacement = Area under a velocity-time graph
- Acceleration is any change in the velocity of an object in a given time
- As velocity is a vector quantity, this means that if the speed of an object changes, or its direction changes, then it is accelerating
- An object that slows down tends to be described as ‘decelerating’
Acceleration = Gradient of a velocity-time graph
Motion of a Bouncing Ball
- For a bouncing ball, the acceleration due to gravity is always in the same direction (in a uniform gravitational field such as the Earth’s surface)
- This is assuming there are no other forces on the ball, such as air resistance
- Since the ball changes its direction when it reaches its highest and lowest point, the direction of the velocity will change at these points
- The vector nature of velocity means the ball will sometimes have a:
- Positive velocity if it is travelling in the positive direction
- Negative velocity if it is travelling in the negative direction
- An example could be a ball bouncing from the ground back upwards and back down again
- The positive direction is taken as upwards
- This will be either stated in the question or can be chosen, as long as the direction is consistent throughout
- Ignoring the effect of air resistance, the ball will reach the same height every time before bouncing from the ground again
- When the ball is travelling upwards, it has a positive velocity which slowly decreases (decelerates) until it reaches its highest point
- At point A (the highest point):
- The ball is at its maximum displacement
- The ball momentarily has zero velocity
- The velocity changes from positive to negative as the ball changes direction
- The acceleration, g, is still constant and directed vertically downwards
- At point B (the lowest point):
- The ball is at its minimum displacement (on the ground)
- Its velocity changes instantaneously from negative to positive, but its speed (magnitude) remains the same
- The change in direction causes a momentary acceleration (since acceleration = change in velocity / time)
The velocity-time graph of a vehicle travelling with uniform acceleration is shown in the diagram below.
Calculate the displacement of the vehicle at 40 s.
Summary of Gradients & Areas
- The gradient of a displacement-time graph is the velocity
- The gradient of a velocity-time graph is the acceleration
- The area under a velocity-time graph is the displacement
- The area under an acceleration-time graph is the velocity
Always check the values given on the y-axis of a motion graph – students often confuse displacement-time graphs and velocity-time graphs.
The area under the graph can often be broken down into triangles, squares and rectangles, so make sure you are comfortable with calculating area!