Graphs of Motion (OCR Gateway GCSE Physics)

Distance-Time Graphs

• A distance-time graph shows how the distance of an object moving in a straight line (from a starting position) varies over time

This graph shows a moving object moving further away from its origin

Constant Speed on a Distance-Time Graph

• Distance-time graphs also show the following information:
  • If the object is moving at a constant speed
  • How large or small the speed is

• A straight line represents constant speed
• The slope of the straight line represents the magnitude of the speed:
  • A very steep slope means the object is moving at a large speed
  • A shallow slope means the object is moving at a small speed
  • A flat, horizontal line means the object is stationary (not moving)

This graph shows how the slope of a line is used to interpret the speed of moving objects. Both of these objects are moving with a constant speed, because the lines are straight.

Changing Speed on a Distance-Time Graph

• Objects sometimes move at a changing speed
  • This is represented by a curve

• In this case, the slope of the line will be changing
  • If the slope is increasing, the speed is increasing (accelerating)
  • If the slope is decreasing, the speed is decreasing (decelerating)

• The image below shows two different objects moving with changing speeds

Changing speeds are represented by changing slopes. The red line represents an object slowing down and the green line represents an object speeding up.

Gradient of a Distance-Time Graph

• The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:

The speed of an object can be found by calculating the gradient of a distance-time graph

•  is the change in y (distance) values
• is the change in x (time) values

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

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:

Velocity-Time Graphs

• A velocity-time graph shows how the velocity of a moving object varies with time
  • The red line represents an object with increasing velocity
  • The green line represents an object with decreasing velocity

Increasing and decreasing velocity represented on a velocity-time graph

Acceleration on a Velocity-Time Graph

• Velocity-time graphs also show the following information:
  • If the object is moving with a constant acceleration/deceleration
  • The magnitude of the acceleration/deceleration

• A straight line represents constant acceleration
• The slope of the line represents the magnitude of acceleration
  • A steep slope means large acceleration (or deceleration) - i.e. the object's speed changes very quickly
  • A gentle slope means small acceleration (or deceleration) - i.e. the object's speed changes very gradually
  • A flat line means the acceleration is zero - i.e. the object is moving with a constant velocity

Interpreting the slope of a velocity-time graph

• The acceleration of an object can be calculated from the gradient of a velocity-time graph

The gradient of a velocity-time graph

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