Motion Graphs

Motion

What is a displacement–time graph?

A graph showing displacement on the y-axis and time on the x-axis.

What is a distance–time graph?

A graph showing distance travelled on the y-axis and time on the x-axis.

What is a velocity–time graph?

A graph showing velocity on the y-axis and time on the x-axis.

What is an acceleration–time graph?

A graph showing acceleration on the y-axis and time on the x-axis.

What does the gradient of a distance–time graph represent?

Speed.

What is the equation for the gradient of a distance–time graph?

Gradient = change in distance ÷ change in time.

How can speed be calculated from a distance–time graph?

Speed = change in distance ÷ change in time.

What does the gradient of a displacement–time graph represent?

Velocity.

How can velocity be calculated from a displacement–time graph?

Velocity = change in displacement ÷ change in time.

What does a steeper gradient on a distance–time graph mean?

A greater speed.

What does a horizontal line on a distance–time graph mean?

The object is stationary because its distance is not changing.

Can a distance–time graph have a negative gradient?

No. Total distance travelled cannot decrease.

Can a displacement–time graph have a negative gradient?

Yes. It means the object is moving in the opposite direction.

What does a positive gradient on a displacement–time graph mean?

The object has a positive velocity and is moving in the chosen positive direction.

What does a negative gradient on a displacement–time graph mean?

The object has a negative velocity and is moving in the opposite direction.

What does a horizontal line on a displacement–time graph mean?

The object is stationary and has zero velocity.

What does a curved distance–time graph indicate?

The object's speed is changing.

How can instantaneous speed be found from a curved distance–time graph?

Draw a tangent to the curve at that point and calculate its gradient.

What does a constant gradient on a displacement–time graph mean?

The object is moving at constant velocity.

What does a velocity–time graph show?

How the velocity of an object changes with time.

What does a horizontal line on a velocity–time graph mean?

The object is moving at constant velocity.

What does a horizontal line at zero on a velocity–time graph mean?

The object is stationary.

What does a positive velocity mean?

The object is moving in the chosen positive direction.

What does a negative velocity mean?

The object is moving in the opposite direction.

What does the gradient of a velocity–time graph represent?

Acceleration.

How is acceleration calculated from a velocity–time graph?

Acceleration = change in velocity ÷ change in time.

What is the equation for acceleration from a velocity–time graph?

a = Δv ÷ Δt.

What does a positive gradient on a velocity–time graph mean?

Positive acceleration.

What does a negative gradient on a velocity–time graph mean?

Negative acceleration.

What does a zero gradient on a velocity–time graph mean?

Zero acceleration and constant velocity.

What does a steeper gradient on a velocity–time graph indicate?

A greater magnitude of acceleration.

How can distance travelled be found from a velocity–time graph?

Calculate the total area between the graph line and the time axis.

Why does the area under a velocity–time graph represent distance or displacement?

Area = velocity × time, and velocity × time gives displacement.

How is displacement found from a velocity–time graph?

Calculate the signed area between the graph and the time axis.

What does an area above the time axis on a velocity–time graph represent?

Positive displacement.

What does an area below the time axis on a velocity–time graph represent?

Negative displacement.

How do you calculate total distance from a velocity–time graph containing negative velocity?

Calculate the magnitude of all areas above and below the time axis and add them together.

How do you calculate displacement from a velocity–time graph containing positive and negative velocity?

Add positive areas and subtract areas below the time axis.

How do you calculate the area of a rectangle on a velocity–time graph?

Area = base × height.

How do you calculate the area of a triangle on a velocity–time graph?

Area = ½ × base × height.

How do you calculate the area of a trapezium on a velocity–time graph?

Area = ½ × (sum of parallel sides) × perpendicular distance.

What does an acceleration–time graph show?

How acceleration changes with time.

What does a horizontal line on an acceleration–time graph mean?

The object has constant acceleration.

What does a horizontal line at zero on an acceleration–time graph mean?

The object has zero acceleration and therefore constant velocity.

What does a negative value on an acceleration–time graph mean?

The acceleration is in the negative direction.

What is the acceleration due to gravity near Earth's surface?

Approximately 9.81 m s⁻² downwards.

What happens to a falling object's velocity if it has constant acceleration due to gravity?

Its velocity changes by approximately 9.81 m s⁻¹ every second.

Why might the acceleration of a falling object decrease as it falls?

Air resistance increases as its speed increases, reducing the resultant force and therefore reducing acceleration.

What happens to a skydiver's acceleration as air resistance increases?

The magnitude of the acceleration decreases towards zero.

Why does a skydiver's acceleration eventually become zero?

Air resistance becomes equal to weight, so the resultant force is zero.

What happens to velocity when acceleration becomes zero during a fall?

The object continues at constant velocity.

What is gradient?

The slope of a graph, calculated as change in y ÷ change in x.

How do you calculate the gradient of a straight line?

Gradient = change in y ÷ change in x.

Why are gradients important in motion graphs?

They can be used to determine quantities such as speed, velocity and acceleration.

What does an increasing gradient on a distance–time graph indicate?

The object is speeding up.

What does a decreasing gradient on a distance–time graph indicate?

The object is slowing down.

What does a straight upward-sloping line on a velocity–time graph indicate?

Constant positive acceleration.

What does a straight downward-sloping line on a velocity–time graph indicate?

Constant negative acceleration.

What happens when a velocity–time graph crosses the time axis?

The velocity changes sign, meaning the object changes direction.