Describe the shape of the displacement–time graph for an object moving at constant velocity.

It is a straight line with a constant gradient, and the steeper the line the greater the velocity.

Describe the shape of the displacement–time graph for an object accelerating uniformly from rest, and explain how the velocity at one instant is obtained from it.

The graph is a curve of steadily increasing gradient, a parabola, because s is proportional to t²; the instantaneous velocity is found from the gradient of the tangent drawn to the curve at that point.

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

The gradient of a velocity–time graph gives the acceleration of the object at that point in the motion.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

Topic overview Physical quantities and SI base units Prefixes and standard form Scalars and vectors Resolving vectors and finding resultants Coplanar forces in equilibrium

Moments and Equilibrium

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Linear Motion and Dynamics

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Newton's Laws of Motion

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Linear Momentum and Impulse

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Thermal Physics

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Uniform Circular Motion

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Simple Harmonic Motion

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The Nucleus and Radioactive Decay

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Fundamental Particles

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Linear Motion and Dynamics

Displacement–time and velocity–time graphs

3 things to know
Unit AS 1

Overview

Recall questions on what the gradient of each graph represents and what the area under a velocity–time graph gives, the shapes for constant velocity and for uniform acceleration, negative gradients and areas below the axis, finding an instantaneous acceleration from a curve, and worked problems on a vehicle and a train.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

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

Key term

What does a horizontal section of a displacement–time graph tell you about the motion?

Key term

What does a negative gradient on a displacement–time graph tell you about the motion?

Questions from this subtopic

Each one with the model answer underneath.

1
What does the gradient of a displacement–time graph represent?
Model answer
The gradient of a displacement–time graph gives the velocity of the object at that point in the motion.
2
Describe the shape of the displacement–time graph for an object moving at constant velocity.
Model answer
It is a straight line with a constant gradient, and the steeper the line the greater the velocity.
3
What does a horizontal section of a displacement–time graph tell you about the motion?
Model answer
The displacement is not changing, so the object is stationary during that interval.
4
What does a negative gradient on a displacement–time graph tell you about the motion?
Model answer
The displacement is decreasing, so the object is moving back in the direction chosen as negative, towards and possibly past its starting point.
5
Describe the shape of the displacement–time graph for an object accelerating uniformly from rest, and explain how the velocity at one instant is obtained from it.
Model answer
The graph is a curve of steadily increasing gradient, a parabola, because s is proportional to t²; the instantaneous velocity is found from the gradient of the tangent drawn to the curve at that point.
6
What does the gradient of a velocity–time graph represent?
Model answer
The gradient of a velocity–time graph gives the acceleration of the object at that point in the motion.

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