Motion Graphs 1

Motion Graphs - Part I

Objectives

• Be able to plot distance-time graphs to show simply journeys for objects moving at constant speeds.

• Be able to interpret distance-time graphs in order to describe and explain the motion of the object.

• Be able to calculate the speed of an object by finding the gradient of a distance-time graph.

Task 1 - Starter Questions

Answer the starter questions below, showing full working for all your calculations:

Q1 A motorcycle travels 820m in 40 seconds. What speed is the motorcycle travelling?

Q2 A snail travels at a speed of 2 cm/s. How long does it take to travel 5 metres? Give your answer in seconds, and then convert it to a sensible unit.

Q3 A car takes 6 seconds to accelerate from 8m/s to 26m/s. What is the car's rate of acceleration?

Q4 A cheetah can accelerate at 8.5 m/s². Calculate the time taken for a cheetah to accelerate:

a) from 10 m/s to 25 m/s.

b) to 25 m/s from rest.

Task 2

We need to be able to draw and interpret two different types of motion graph. The first is a distance-time graph, which gives us information about the position of an object. We will also learn how to obtain information about the object's speed from this type of graph.

Listen carefully as your teacher explains how distance-time graphs are plotted and how we can interpret the information on the graph, using this presentation.

Task 3 - collecting data

We are going to collect some data about the position of a wind-up toy snake as it moves along the bench, in order to plot our own distance-time graph.

Draw a table, like the one below, in your exercise book.

Distance (cm)	Time (s)
0
20
40
60
80
100
120
140
160
180
200
220
240

Your teacher will ask some of you to measure the time taken for the snake to reach the various positions along bench.

Task 4 - graphing motion

Draw a graph of distance (y-axis) against time (x-axis) for the data you have collected. When you have finished, draw a line of fit through your points. It should have a straight section near the beginning, and a curved section near the end.

1. Complete the sentences below:

The toy snake travelled a total distance of _________ cm

The total time taken was _________ seconds.

2. Use the formula you learned to calculate the average speed of the toy snake. Show full working for your calculation.

3. Can you explain why it is only an average speed? Was the snake travelling faster or slower than this at the beginning of its journey? What about at the end of the journey?

Task 5 - calculating gradients

You should recognise that the snake was travelling faster at the beginning of the journey than the end. We are going to try to find out the speed near the beginning and end of the journey.

We will do this using the rule below. Write the rule in your exercise in large lettering and draw a box around it.

The gradient of a distance-time graph is the speed.

You may have already learned how to calculate gradients in your mathematics classes, but your teacher will remind you how to do this!

Start by writing the formula for calculating gradients somewhere on your graph:

gradient = increase in y ÷ increase in x

We are going to find the gradient at two different points on the graph. You teacher will explain in detail how to find a gradient on the straight section of the line near the beginning. Follow all the steps carefully and draw the lines accurately with a pencil and ruler!

Write the gradient you have calculated on your graph. Remember to include units with it!

Now, you will need to find the gradient further along the line, where it starts to level off. Follow the same process as last time. Once again, draw the lines carefully with a pencil and ruler and show all working for your calculation.

Homework

You will need to practise drawing distance time graphs. Plot a distance-time graph of the data on this presentation. Your teacher will also give you a copy of the data to stick in your exercise book.

Time (s)	Distance (m)
0	0
10	75
20	150
30	225
50	300
70	375
90	450

Now, you should see from your graph that the cyclist has moved at two distinct speeds during his journey. Draw two straight lines of fit to show this.

1. Find the gradient and hence the cyclist’s speed during the first part of the journey.

2. 2.Find the gradient, and hence the cyclist’s speed during the second part of the journey.

3. Calculate the cyclist’s average speed, either by finding a gradient or otherwise.