# Introduction

In this activity you will:

- explore how the displacement of a moving object can be represented using a displacement-time graph;
- discover what a displacement-time graph can tell you about the velocity of the object;
- find out about the distinction between
*displacement*and*distance*; - see that
*distance*can have different meanings in different contexts.

# Moving

You should have noticed that the graph is steeper when the skateboard moves faster, and that it is horizontal when the skateboard isn't moving.

Position is a **vector** quantity - it has direction as well as magnitude. Moving to the left of the starting point gives you a negative position.

The skateboard icon can be moved along the line at the bottom of the window on the right. The graph is a plot of the **position** of the skateboard on the line, against **time**.

Move the skateboard along the line.

- How is the graph affected if you move it faster?
- What happens if you stop moving the skateboard?
- What about if you change its direction?

The **Reset** button will clear the graph so that you can try again. When you have finished investigating, **Finish**.

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# Displacement

You have correctly used the idea of displacement from the original position.

On the last page, the graph showed **position** (a vector quantity) plotted against **time** (a scalar quantity). Position is given in reference to an origin on a line.

The **displacement** of an object is about changing from one position to another, and is *final position* - *initial position*. It is a **vector quantity**. You usually need to state where displacement is from.

The graph shows the journey of a particle moving on a straight line. At time $$t = 6$$, the displacement of the particle from point A is $$-2$$ m. At time $$t = 10$$, the displacement of the particle from point A is $$1$$ m.

Move the green points so that

- at time , the displacement of the particle from point A is

$$1$$ m - at time , the displacement of the particle from point A is $$-2$$ m.

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# A simple graph

Well done! When the velocity is

3 m s^{-1}, the displacement after 10 seconds is 30 metres.

On this page you will explore the displacement-time graph for the journey of a particle moving in a straight line for 10 seconds at constant velocity.

Click the journey buttons on the screen as they appear, and follow the on-screen instructions.

When you have finished, **Submit**.

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# Speedy

AB is the part of the graph where the speed is greatest, because the magnitude of the gradient of the line AB is largest. Notice that the gradient of AB is negative, so the object is moving in a negative direction then, and so it has negative velocity.

BC is the part of the graph where the velocity is greatest, because the gradient of the line AB is largest.

On the previous page, you saw that the gradient of a displacement-time graph tells you the velocity of the moving object.

Velocity is a **vector** quantity. Speed is a **scalar** quantity, and the speed is the magnitude of the velocity.

The diagram shows the displacement-time graph for a particle moving in a straight line.

For which part of the graph is the speed of the particle greatest, and for which part of the graph is the velocity of the particle greatest? Tick the box for OA, AB or BC in each case.

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# Distances

For each graph, you need to add up the distances travelled for each part of the graph.

Q has travelled the greatest distance in total.

The **distance travelled** (a scalar quantity) is the sum of the distances travelled in either direction.

The diagram shows displacement-time graphs for the journeys of three particles, P, Q and R, all of which are travelling in a straight line. The displacements are measured from the origin.

Which of the particles travels the greatest distance in total during its journey? Tick the box for P, Q or R.

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# Displacement and distance

You have understood the difference between displacement, total distance travelled and distance of final position from the start.

Gemma is walking on a straight road. The displacement-time graph shows her displacement from her home.

The graph shows that when $$t=0$$, Gemma's displacement from her home is $$20$$ m.

Fill in the blanks in the statements under the diagram. Remember that displacement is a **vector** quantity and **distance** is a scalar quantity.

# There and back again

You have constructed the displacement-time graph correctly.

Press the **Show motion** button to see the motion of particle P, a description of its motion in words and also its displacement-time graph.

When the graph has finished, press the **Change motion** button and move the points B, C and D so that the graph represents a new journey as follows (note that point C can only be moved horizontally):

- Particle P moves at $$3$$ m s
^{-1}for $$2$$ seconds - then is stationary for $$3$$ seconds
- then moves at $$-1$$ m s
^{-1}for $$3$$ seconds

You can use the **Show motion** button to see the description of your graph. When you are happy with it, press **Submit**.

Created with GeoGebra

# Describing the journey

Have a look at the answers that you got wrong, and try to correct them.

You have described the journey correctly.

The diagram shows the displacement-time graph for the journey of a particle.

Fill in the blanks below the diagram to describe the journey.

# Finally...

Youâ€™ve now completed this activity. Go and explore the other resources!

In this walkthrough you have learned that for motion in a straight line:

**position**and**displacement**are vector quantities, whereas**distance**is a scalar quantity;- in a position-time graph or a displacement-time graph, the gradient of the graph represents the velocity;
- displacement means
*final position*-*initial position*, and can be negative; - distance can have different meanings in different contexts: distance can mean
*magnitude of displacement*, while distance travelled means the sum of the distances travelled in either direction.