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# Speed and velocity for SQA Higher Physics

This page covers the following topics:

1. Speed and velocity

2. Speed from graphs

3. Velocity from graphs

Speed is the amount of distance covered by an object per unit time. It is calculated by dividing the distance travelled by the time taken. The standard units of speed are metres per second (m/s). Speed is a scalar quantity, since it is only described by magnitude. When the motion of an object is non-uniform, ie. it is not travelling at a constant speed, the average speed can be calculated by dividing the total distance travelled by the total time taken.

Velocity is the speed of an object in a given direction, thus velocity is a vector quantity. Velocity has the same standard units as speed, m/s. Velocity-time graphs can be drawn to model the motion of an object. If the velocity of an object is changing, the velocity value on the graph decreases or increases. A horizontal line in the velocity-time graph indicates that the velocity is not changing.

The motion of an object in a straight line can be modelled using a distance-time graph. The gradient of a distance-time graph at a specific point in time is the speed of the object at that time. The speed of an object from a straight line in a distance-time graph can be found by dividing the change of distance by the in time between two points. An accelerating object can be modelled on distance-time graph using curved lines.

Acceleration-time graphs can be sketched to model the acceleration of an object over time. The area under an acceleration-time graph represents the change in velocity over a given period of time for the object. A flat line on an acceleration-time graph means that the object is travelling at a constant acceleration.

# 1

Rebecca lives 550 m away from her school. Given that Rebecca walks to school in 6 minutes, calculate the average speed of her motion.

6 minutes = 360 seconds

speed = distance รท time

speed = 550 m รท 360 s = 1.53 m/s (to 3 sf)

1.53 m/s

# 2

An object is travelling at a constant speed for 15 seconds, during which it travels through 7 m. The object is then stationary for 5 seconds, and finally accelerates for another 10 seconds, reaching 20 m at the end of its journey. Sketch a distance-time graph to model this journey.

In the first 15 seconds, the object is moving at a constant speed, therefore the gradient of the graph is positive and constant. In the next 5 seconds, the object is stationary, therefore the graph is flat. In the last 10 seconds, the object is accelerating, therefore the gradient is increasing.

image

# 3

The motion of an object is modelled by the given velocity-time graph. Describe object's velocity at 600 s.

A horizontal line in the velocity-time graph indicates that the velocity is not changing.

constant velocity

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