• 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 might be moving 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

• The?rise?is the?change?in y (distance) values
• The?run?is the?change?in x (time) values

Step 1: Draw a large gradient triangle on the graph and label the magnitude of the rise and run

• • The image below shows a large?gradient triangle?drawn with dashed lines
  • The?rise?and?run?magnitude is labelled, using the?units?as stated on each axes

   

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

• • The distance travelled (rise) = 8 km =?8000 m
  • The time taken (run) = 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 in to calculate the speed

speed = gradient = 8000 ÷ 360

speed =?22.2 m/s

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: