12.06 Distance time graphs

Distance-time graphs are a way to describe the movement of people or objects. They usually describe a trip that leaves and returns to a point (like a home base).

The vertical axis of a distance-time graph is the distance travelled from a starting point and the horizontal axis is the time taken from the starting point.

 

Reading a distance-time graph

There are certain important features of a distance-time graph that we can use to interpret the journey being described:

• As the line moves away from the horizontal axis, the object is moving further away from the "home" point
• As the line moves back towards the horizontal axis, the object is returning home
• When the line is horizontal, the object is not moving
• The steeper the line, the greater the speed of the an object (the faster it moves)
• A straight non-horizontal line indicates a steady speed
• The total distance of the trip is the distance away from home plus the distance returning home

 

Worked example

Consider the following graph which displays a day long car tip with the horizontal axis being time in hours and the vertical axis being distance from home in kilometres:

(a) What speed did the car travel in the first hour?

Think: We know that $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$Speed=DistanceTime​. We need the distance travelled in the first hour.

Do:

Speed	$=$=	$\frac{\text{Distance}}{\text{Time}}$DistanceTime​
	$=$=	$\frac{80\text{ km}}{1\text{ h}}$80 km1 h​
	$=$=	$80$80 km/h

(b) What happened between the times of $1$1 and $2$2?

Think: What does it mean for the graph to be horizontal?

Do: The car was stationary for $1$1 hour. Perhaps a break for lunch or a visit to a park.

 

(c) How far is the car from home after $6$6 hours?

Think: Locate the dot at $6$6 hours. Look across to the vertical axis to find the distance at this time.

Do: The car is $50$50 km from home.

 

(d) What was the average speed of the car over the $6$6 hour journey?

Think: How far has the car travelled in total? The car initially travelled $80$80 km, then was stationary for one hour, then travelled a further $120$120 km before starting the return tip home at $4$4 hours into the journey. In the last section of the journey they are returning to home from $200$200 kilometres away and reach $50$50 kilometres from home, thus they travel $150$150 km.

Do:

Total distance travelled	$=$=	$80+120+150$80+120+150 km
	$=$=	$350$350 km

 

Average speed	$=$=	$\frac{\text{Total distance}}{\text{time}}$Total distancetime​
	$=$=	$\frac{350\ km}{6\ h}$350 km6 h​
	$=$=	$58.\overline{3}$58.3 km/h

 

Practice questions

Question 1

Question 2

Question 3