Gradients

• The gradient of a?displacement-time graph is the?velocity
• The gradient of a?velocity-time graph is the?acceleration

Area Under the Graph

• The area under a?velocity-time graph is the?displacement
• The area under an?acceleration-time graph is the?velocity

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)