Displacement & Velocity-Time Graphs (OCR A Level Physics)

Displacement-Time Graphs

• 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)

Velocity-Time Graphs

• 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)

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