Graphs of Motion (OCR GCSE Physics A (Gateway))

A distance-time graph is drawn below for part of a train journey. The train is travelling at a constant speed.

Calculate the speed of the train.

Answer:

Step 1: Draw a large gradient triangle on the graph

• The image below shows a large gradient triangle drawn with dashed lines

• and are labelled, using the units as stated on each axis

Step 2: Convert units for distance and time into standard units

• The distance travelled  = 8 km = 8000 m

• The time taken  = 6 mins = 360 s

Step 3: State that speed is equal to the gradient of a distance-time graph

• The gradient of a distance-time graph is equal to the speed of a moving object:

Step 4: Substitute values to calculate the speed

Ose decides to take a stroll to the park. He finds a bench in a quiet spot and takes a seat, picking up where he left off reading his book on Black Holes.After some time reading, Ose realises he lost track of time and runs home.A distance-time graph for his trip is drawn below:

a) How long does Ose spend reading his book? There are three sections labelled on the graph: A, B and C.

b) Which section represents Ose running home?

c) What is the total distance travelled by Ose?

Answer:

Part (a)

• Ose spends 40 minutes reading his book

• The flat section of the line (section B) represents an object which is stationary - so section B represents Ose sitting on the bench reading

• This section lasts for 40 minutes - as shown in the graph below

Part (b)

• Section C represents Ose running home

• The slope of the line in section C is steeper than the slope in section A

• This means Ose was moving with a larger speed (running) in section C

Part (c)

• The total distance travelled by Ose is 0.6 km

• The total distance travelled by an object is given by the final point on the line - in this case, the line ends at 0.6 km on the distance axis. This is shown in the image below:

Tora is training for a cycling tournament.

The velocity-time graph below shows her motion as she cycles along a flat, straight road.

(a) In which section (A, B, C, D, or E) of the velocity-time graph is Tora’s acceleration the largest?

(b) Calculate Tora’s acceleration between 5 and 10 seconds.

Answer:

Part (a)

Step 1: Recall that the slope of a velocity-time graph represents the magnitude of acceleration

• The slope of a velocity-time graph indicates the magnitude of acceleration

  Therefore, the only sections of the graph where Tora is accelerating is section B and section D

• Sections A, C, and E are flat – in other words, Tora is moving at a constant velocity (i.e. not accelerating)

Step 2: Identify the section with the steepest slope

• Section D of the graph has the steepest slope

  Hence, the largest acceleration is shown in section D

Part (b)

Step 1: Recall that the gradient of a velocity-time graph gives the acceleration

• Calculating the gradient of a slope on a velocity-time graph gives the acceleration for that time period

Step 2: Draw a large gradient triangle at the appropriate section of the graph

• A gradient triangle is drawn for the time period between 5 and 10 seconds below:

Step 3: Calculate the size of the gradient and state this as the acceleration

• The acceleration is given by the gradient, which can be calculated using:

acceleration = gradient = 5 ÷ 5 = 1 m/s²

• Therefore, Tora accelerated at 1 m/s² between 5 and 10 seconds

Use the entire line, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used - so remember to draw 'rise' and 'run' lines directly on the graph itself!