Distance, speed and time
Apply the formula D = ST to find distance, speed or time; solve multi-leg journey problems to find average speed; and substitute into stopping distance formulas to interpret and compare results.
Worked examples
Finding distance using D = ST
Straightforward
Problem
A car travels at 70 km/h for 3 hours. Find the distance travelled.
1
Write the formula.
2
Identify the values: speed km/h and time hours.
,
3
Substitute and evaluate.
Answer
Average speed for a two-leg journey
Moderate
Problem
A car travels 100 km at 50 km/h, then a further 150 km at 75 km/h. Find the average speed for the whole journey.
1
Find the time for the first leg using .
2
Find the time for the second leg.
3
Find the total distance and total time.
Total distance km
Total time hours
Total time hours
4
Calculate the average speed.
Answer
Comparing stopping distances using a formula
Challenging
Problem
The stopping distance metres for a vehicle travelling at km/h is given by . Find the stopping distances at 50 km/h and 100 km/h. By how many metres does the stopping distance increase when speed doubles?
1
Substitute into the formula.
2
Substitute into the formula.
3
Find the increase in stopping distance.
4
Interpret the result.
Doubling the speed from 50 km/h to 100 km/h increases the stopping distance by 485 m. The stopping distance at 100 km/h is times the stopping distance at 50 km/h — far more than double — because the term grows with the square of speed.
Answer
Stopping distance increases by
Practise
Q1·Straightforward
A car travels at a constant speed of 60 km/h for 4 hours. How far does it travel in km?
Explanation
Q2·Straightforward
A cyclist covers 90 km at a constant speed of 18 km/h. How many hours does the journey take?
Explanation
Q3·Straightforward
A train travels 280 km in 3.5 hours. What is its average speed in km/h?
Explanation
Q4·Straightforward
A runner jogs at 8 km/h for 45 minutes. How far does the runner travel in km?
Explanation
Convert time: hours.
Q5·Moderate
A car travels 100 km at 50 km/h, then 120 km at 60 km/h. How many hours does the whole journey take?
Explanation
Time for first leg: hours.
Time for second leg: hours.
Time for second leg: hours.
Q6·Moderate
A bus travels 90 km at 45 km/h, then a further 60 km at 30 km/h. What is the average speed for the whole journey in km/h?
Explanation
Time for first leg: hours.
Time for second leg: hours.
Total distance km. Total time hours.
Time for second leg: hours.
Total distance km. Total time hours.
Q7·Moderate
A cyclist rides at 24 km/h for 1.5 hours, then at 18 km/h for 2 hours. What is the total distance in km?
Explanation
Distance for first leg: km.
Distance for second leg: km.
Distance for second leg: km.
Q8·Moderate
A boat travels 80 km upstream at 20 km/h and then returns 80 km downstream at 40 km/h. What is the average speed for the round trip in km/h? Give your answer to two decimal places.
Explanation
Time upstream: hours.
Time downstream: hours.
Total distance km. Total time hours.
Time downstream: hours.
Total distance km. Total time hours.
Q9·Challenging
The stopping distance metres for a vehicle travelling at km/h is given by the formula . Calculate the stopping distance when km/h.
Explanation
Q10·Challenging
Using the stopping distance formula , calculate the stopping distance in metres when km/h.
Explanation
Q11·Challenging
Using , by how many metres is the stopping distance at 80 km/h greater than the stopping distance at 50 km/h?
Explanation
At : m.
At : m.
At : m.
Q12·Challenging
Using the formula , a vehicle travelling at 60 km/h has a stopping distance of 258 m, and at 90 km/h has a stopping distance of 549 m. Which statement correctly describes how the stopping distance changes?
Explanation
At 60 km/h: m.
At 90 km/h: m.
The stopping distance at 90 km/h is about 2.13 times the stopping distance at 60 km/h — more than double. This shows that a 50% increase in speed leads to more than a doubling of stopping distance, because the term grows much faster than .
At 90 km/h: m.
The stopping distance at 90 km/h is about 2.13 times the stopping distance at 60 km/h — more than double. This shows that a 50% increase in speed leads to more than a doubling of stopping distance, because the term grows much faster than .