**Distance-time**graphs show distance from a fixed point at different times- Distance is on the vertical axis, and time is on the horizontal axis.

- The
**gradient**of the graph is the**speed** - A
**positive gradient**represents the object (or person)**moving away**from the starting point - If the graph is a
**horizontal**line the object is**stationary**(not moving) - A
**negative gradient**represents the object (or person)**moving towards**the starting point - If the graph is a
**straight****line**the**speed is constant** - If the graph is a
**curve**you can find an estimate of the**speed at a point**by drawing the**tangent**at a point on the graph and find its**gradient** - To find the
**average speed**through a period of time, divide the**total distance**in that time period by the**total time**

- It is easy to get confused between different types of graph.
- Look at the label on the vertical axis to make sure you are looking at a DISTANCE-time graph (not speed-time)

One afternoon Mary cycled to her grandparents' house, 8 km from her own home.

Part of her travel graph for her journey is shown below.

Mary stayed at her grandparents' house for half an hour.

She then cycled home at a steady speed, without stopping, arriving home at 4 pm.

a)

Complete the travel graph for Mary's journey.

Begin by checking the scale on the time axis. Note that one square is 15 minutes.

Mary stays at her grandparents' house for 30 minutes, so draw a horizontal line for 2 squares to show this.

Her cycle home is represented by a straight line (steady speed) drawn from the end of her stay to 4pm on the time axis (where the distance from home is zero).

b)

For how long did Mary stop on the way to her grandparents' house?

Mary's stop on the way is the short horizontal line from 1.30 pm to 1.45 pm. The horizontal line is one square long so represents 15 minutes.

c)

What is Mary's speed between 1.45 pm and 2.45 pm?

Speed can be found on a distance-time graph by finding the gradient of the line at that point.

**Speed-time**graphs show speed at different times- Speed is on the vertical axis, and time is on the horizontal axis

- The
**gradient**of the graph is the**acceleration** -
- If the graph is a
**curve**you can- estimate of the
**acceleration at a point**by drawing the**tangent**at that point on the graph and finding its**gradient** - find the
**average acceleration**between two points by drawing a**chord**between the two points and finding its**gradient**

- estimate of the
- A
**positive gradient**shows positive acceleration (speeding up) - A
**horizontal**line on a**speed-time**graph shows**constant speed**(no acceleration) - A
**negative gradient**shows negative acceleration, or**deceleration**(slowing down)

- The
**distance**covered can be found by finding the**area under the graph** - If the graph is a
**curve**you can estimate the distance covered by drawing trapeziums underneath the graph and finding their area

- It is easy to get confused between different types of graph.
- Look at the label on the vertical axis to make sure you are looking at a SPEED-time graph (not distance-time)

The speed-time graph for a car travelling between two sets of traffic lights is shown below.

a)

Calculate the acceleration in the first 6 seconds.

In a speed-time graph the acceleration is the gradient of the graph.

b)

Work out the distance covered by the car.

In a speed-time graph the distance travelled is equal to the area under the graph.

The graph is a trapezium so use the formula .

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