# 3. Using the Gradient to Calculate Speed

# Success Criteria

Your learning has been successful if you can do the following:

Calculate the average speed of an object from the gradient of a distance-time graph.

# Vocabulary

Learn these so you can communicate this concept well.

Average speed: Calculated by the total distance travelled divided by the total time taken for the journey.

Gradient / slope: How steep a line on a graph is.

Speed: How fast an object is moving.

Velocity: Similar to speed, but also tells us the direction in which an object is moving. It includes both speed and direction of motion.

Do Now:

Collect and complete this small 'Do Now'. Then glue into your SciPAD page 11. Use your commonsense when glueing - don't glue straight on-top of words!

Find some space on page 15 of your PESS1.2 SciPAD,

and answer the following questions:

What does each letter in CUTLASS stand for?

## Distance-Time Graphs

The size of the SLOPE (GRADIENT) of the graph gives the speed.

The steeper the slope the greater the speed.

The flatter the slope, the lower the speed.

The sign of the slope (+ or -) gives the direction of a moving object.

A positive slope (+) means the object is moving away from the starting point.

A negative slope (-) means the object is moving back towards the starting point.

SPEED plus direction gives the VELOCITY of an object (e.g. 50 m/s East).

Example 1

The graph below is a distance-time graph for the motion of a radio-controlled toy car. The shape of the graph tells you that the car is travelling at a constant speed. You can also calculate the speed of the car at various time intervals by finding the slope or gradient of this line graph.

Example 1

The graph below is another distance-time graph for the motion of a different radio-controlled toy car.

## Calculating Average Speed

In reality, it is difficult for a vehicle to travel at a constant speed for long. So, we calculate the AVERAGE SPEED, which is the total distance travelled divided by the the total time taken for the journey.

The distance-time graph below shows an object moving at different speeds over the journey. We can calculate its average speed over the entire journey by using the following equation: