Real-life graphs

The graph shows the velocity, v m/s, of a particle t seconds after it starts to move.

Work out an estimate of the gradient of the graph at t = 3 You must show how you get your answer.

What does this gradient represent?

Work out an estimate for the distance the particle travelled in the first 6 seconds. Use 3 strips of equal width.

A train travels from Derby to Sheffield. The travel graph shows information about the train’s journey.

Work out the speed of the train. Give your answer in miles per hour.

The train stays at Sheffield for 15 minutes.

Show this information on the travel graph.

Amy walked from her home to the skate park. The travel graph of Amy’s walk to the skate park is shown below.

Time On the way to the skate park Amy stopped at her friend’s house.

How far is it from her friend’s house to the skate park?

Amy stayed at the skate park for 2 hours. Then she walked home at a steady speed. She took 1 hour 30 minutes to walk home.

Complete the travel graph.

You can use this graph to change between miles and kilometres.

kilometres

Change 10 miles into kilometres.

Rob drives 17 miles from Bridlington to Scarborough. He then drives 50 kilometres from Scarborough to Staithes.

What is the total distance Rob drives? Give your answer in miles.

Here is a velocity-time graph for an aeroplane.

Work out an estimate for the distance the aeroplane travelled in the first 30 seconds. Use 3 strips of equal width.

You can use this graph to change between ounces and grams.

Change 6 ounces to grams.

Change 1 kg to ounces.

The graph shows the velocity of a car, in metres per second, t seconds after it starts to slow down.

Calculate an estimate for the acceleration of the car when t = 5 You must show all your working.

Work out an estimate for the distance the car travels in the first 6 seconds after it starts to slow down. Use 3 strips of equal width.

An object falls from rest. Here is the distance‑time graph for the distance (d metres) fallen by the object t seconds after it starts to fall.

Work out an estimate for the gradient of the graph at t = 3 You must show how you get your answer.

This graph can be used to find the cost of parking a car in a car park for up to 12 hours.

Use the graph to find the cost of parking a car for 4 hours.

Justin drives into the car park at 08 00 in the morning. When he drives out of the car park he has to pay £9

At what time does Justin drive out of the car park?

Rowena drove from her home to a beach. Here is a travel graph for her journey.

Rowena stopped at a cafe on her way to the beach.

How many minutes did Rowena take to drive to the cafe?

Write down the distance from Rowena’s home to the cafe.

Rowena stayed at the beach for 1 hours. She then drove home without stopping. Rowena arrived home at 16 00

On the grid, complete the travel graph.

Work out the average speed for the journey from the beach to Rowena’s home.

Here is a distance-time graph.

Find an estimate of the gradient of the graph at time 2.5 seconds. You must show how you get your answer.

What does the gradient of the graph represent?

19Sana needs to draw the graph of y = 3^x for 0 ≤ x ≤ 4 She draws the graph shown on the grid.

Write down one thing Sana has done wrong.

The graph below gives the volume, in litres, of water in a container t seconds after the water starts to fill the container.

Calculate an estimate for the gradient of the graph when t = 17.5 You must show how you get your answer.

Describe fully what the gradient in part (a) represents.

You can use this graph to change between ounces and grams.

Change 850 grams to ounces.

Change 80 ounces to grams.

Carly cycles to her friend’s house. She stays at her friend’s house for a number of minutes. Then she cycles home. Here is the travel graph for her journey.

For how many minutes did Carly stay at her friend’s house?

How far is Carly from her home at 08 50?

Work out Carly’s speed, in km/h, for the first 20 minutes of her journey.

Here is a speed-time graph.

Work out an estimate of the gradient of the graph at t = 2

What does the area under the graph represent?

Nazima uses this graph to find out how much money she is paid for the number of hours she has worked.

How much money is Nazima paid for each hour she works?

Last week Nazima worked for 36 hours.

How much money was Nazima paid?

Sam drives his car on a journey. Here is the travel graph for the first 15 minutes of his journey.

Work out Sam’s speed, in km/h, for the first 15 minutes of his journey.

At 10 15 Sam stops for 10 minutes and then drives for 20 minutes at a speed of 75 km/h.

On the grid, complete the travel graph for Sam’s journey.

Sam drives his car on a journey. Here is the travel graph for the first 15 minutes of his journey.

Work out Sam’s speed, in km/h, for the first 15 minutes of his journey.

At 10 15 Sam stops for 10 minutes and then drives for 20 minutes at a speed of 75 km/h.

On the grid, complete the travel graph for Sam’s journey.

The graph gives the volume of water, in litres, in a container at time t seconds after the water started to flow out of the container.

Using the graph, work out an estimate for the rate at which the water is flowing out of the container when t = 12 You must show your working.

_........ litres per second

Here is a speed-time graph showing the speed, in metres per second, of an object t seconds after it started to move from rest.

Using 3 trapeziums of equal width, work out an estimate for the area under the graph between t = 1 and t = 4

What does this area represent?

The graph shows information about the time, in minutes, a liquid has been cooling and the temperature of the liquid in ° C.

What is the temperature of the liquid at time 2 minutes?

Pam recorded the time when the liquid had a temperature of 50° C.

Write down this time.

Pam says that the temperature of the liquid drops more in the first 3 minutes of cooling than it does between time 9 minutes and time 12 minutes.

Is Pam correct? Give a reason for your answer.

18This graph can be used to change between US dollars ($) and British pounds (£).

Rosie bought a ring in the USA. She paid 345 US dollars. Work out in pounds the amount Rosie paid for the ring.

Here is a speed-time graph for a car.

Work out an estimate for the distance the car travelled in the first 30 seconds.

Is your answer to part (a) an underestimate or an overestimate of the actual distance the car travelled in the first 30 seconds? Give a reason for your answer.

Julian used the graph to answer this question. Work out an estimate for the acceleration of the car at time 60 seconds. Here is Julian’s working. acceleration = speed ÷ time = 13 ÷ 60

Julian’s method does not give a good estimate of the acceleration at time 60 seconds.

Explain why.

Here is a speed-time graph for a train journey between two stations. The journey took 100 seconds.

Calculate the time taken by the train to travel half the distance between the two stations. You must show all your working.

Compare the acceleration of the train during the first part of its journey with the acceleration of the train during the last part of its journey.

The graph shows information about part of a cyclist’s journey.

Work out an estimate of the speed, in m/s, of the cyclist at time 6 seconds.

A car moves from rest. The graph gives information about the speed, v metres per second, of the car t seconds after it starts to move.

Calculate an estimate of the gradient of the graph at t = 15

Describe what your answer to part (i) represents.

Work out an estimate for the distance the car travels in the first 20 seconds of its journey. Use 4 strips of equal width.

Tom uses his lorry to deliver bricks.

You can use this graph to find the delivery cost for different distances.

For each delivery, there is a fixed charge plus a charge for the distance.

How much is the fixed charge?

Tom makes two deliveries of bricks. The distance of one delivery is 20 miles more than the distance of the other delivery.

Work out the difference between the two delivery costs.

The distance-time graph shows information about part of a car journey.

Use the graph to estimate the speed of the car at time 5 seconds.

The graph shows the speed of a car, in metres per second, during the first 20 seconds of a journey.

Work out an estimate for the distance the car travelled in the first 20 seconds. Use 4 strips of equal width.

Is your answer to part (a) an underestimate or an overestimate of the actual distance the car travelled in the first 20 seconds? Give a reason for your answer.

Here is part of a distance-time graph for a car¶s journey.

Between which two times does the car travel at its greatest speed? Give a reason for your answer.

Work out this greatest speed.

Here is a speed-time graph for a train.

Work out an estimate for the distance the train travelled in the first 20 seconds. Use 4 strips of equal width.

Is your answer to (a) an underestimate or an overestimate of the actual distance the train travelled? Give a reason for your answer.

The diagram shows part of the graph of y = x² – 2x + 3

By drawing a suitable straight line, use your graph to find estimates for the solutions of x² – 3x – 1 = 0

P is the point on the graph of y = x² – 2x + 3 where x = 2

Calculate an estimate for the gradient of the graph at the point P.

Complete the table of values for y

On the grid below, draw the graph of y = for values of x from 0.5 to 6