• Three types of graphs that can represent motion are?displacement-time?graphs,?velocity-time?graphs, and?acceleration-time?graphs

Displacement-Time Graph

• On a?displacement-time graph…
  • Slope?equals?velocity
  • The?y-intercept?equals the?initial displacement
  • A?straight(diagonal) line represents a?constant?velocity
  • A?curved?line represents an?acceleration
  • A?positive?slope?represents motion in the?positive?direction
  • A?negative?slope?represents motion in the?negative?direction
  • A?zero?slope (horizontal line) represents a state of?rest
  • The area under the curve is meaningless

Displacement-time graphs displacing difference velocities

Velocity-Time Graph

• On a?velocity-time graph…
  • Slope?equals?acceleration
  • The?y-intercept?equals the?initial velocity
  • A?straight?line represents?uniform?acceleration
  • A?curved?line represents?non-uniform acceleration
  • A?positive?slope represents an?increase?in?velocity?in the?positive?direction
  • A?negative?slope represents an?increase?in?velocity?in the?negative?direction
  • A?zero?slope (horizontal line) represents motion with?constant?velocity
  • The?area?under the curve equals the?change?in?displacement

Velocity-time graphs displacing different acceleration

Acceleration-Time Graph

• On an?acceleration-time graph…
  • Slope is meaningless
  • The?y-intercept?equals the?initial acceleration
  • A?zero slope?(horizontal line) represents an object undergoing?constant acceleration
  • The?area?under the curve equals the?change?in?velocity

How displacement, velocity and acceleration graphs relate to each other

Part (a)

Step 1:?Recall that the slope of a velocity-time graph represents the magnitude of acceleration

• • • The slope of a velocity-time graph indicates the magnitude of accelerationTherefore, the only sections of the graph where Tora is accelerating is section B and section D
    • Sections A, C, and E are flat – in other words, Tora is moving at a constant velocity (i.e. not accelerating)

Step 2: Identify the section with the steepest slope

• • • Section D of the graph has the steepest slope
    • Hence, the largest acceleration is shown in?section D

Part (b)

Step 1: Recall that the gradient of a velocity-time graph gives the acceleration

• • • Calculating the gradient of a slope on a velocity-time graph gives the acceleration for that time period

Step 2: Draw a large gradient triangle at the appropriate section of the graph

• • • A gradient triangle is drawn for the time period between 5 and 10 seconds below:

Step 3: Calculate the size of the gradient and state this as the acceleration

• • • The acceleration is given by the gradient, which can be calculated using:

acceleration = gradient = 5 ÷ 5 = 1 m/s²

• • • Therefore, Tora accelerated at 1 m/s²?between 5 and 10 seconds

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 traveling in the positive direction
  • Negative velocity?if it is traveling 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 traveling 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)