Distance, Speed and Time
Convert the following speed units:
1.
2.
3.
4.
5.
Change 33km/h to
Change 100m/s to
Change 40m.p.h to
Change 90km/h to
Change 100m/s to
a) km/min
a) km/s
a) miles/min
a) km/s
a) m/h
b) m/h
b) m/min
b) miles/s
b) m/s
b) km/h
Distance Time Graphs
Draw distance time graphs to show the following journeys. Show the required working and
where necessary, give answers correct to 3s.f.
1. A train leaves from York and travels at 40km/h for 3 hours. It stops for half an hour and
then returns back to York at 50km/h. Draw a graph to illustrate this journey. Use 2cm for
1 hour and 2cm for 50km. What is the average speed for
a) the journey before going back to York?
b) the whole journey?
2. A cyclist leaves home and rides at 15km/h for 2 hours. He rests for ½ hour and then
continues riding away from home at 12km/h for 1 ½ hours. He has another rest of ½ hour
before returning home, without stopping, at 20km/h.
a) For how long is the cyclist away from home?
b) Draw a graph to illustrate this journey. Use 2cm for 1 hour and 1cm for 10km.
c) What is the average speed for the journey before going back to home?
d) What is the average speed for the whole journey?
3. A bus leaves the bus station at 10:00a.m. It travels at 30km/h for ½ hour, then stops for
12 minutes, before continuing at 40km/h for 2 hours.
a) How far has the bus travelled from the bus station now?
b) Draw the graph to illustrate the journey. Use 2cm for 1 hour and 1cm for 10km.
c) What is the average speed for the whole journey?
4. A family travel by car from town A to town B 50km away, in 48 minutes. They stop in
town B for 1 hour and then continue to village C, which is 70km from B, at a speed of
50km/h. The family stop at C for 2 hours and then return, without stopping, along the
same route to A at 60km/h.
a) Draw the graph to illustrate the journey. Use 3cm for 1 hour and 1cm for 10km.
b) What is the speed of the journey from A to B and the time taken for the return
journey from C to A?
Velocity Time Graphs
Worked example: A car accelerates from rest at 5m/s2 for 6 seconds and then travels at a
constant velocity for 10 seconds after which it decelerates to rest at 3m/s 2. Represent this
information by drawing a velocity time graph. Use 2cm for 5 seconds and 2cm for 5m/s.
1. From O to A, the car reached a
velocity of 30m/s after 6
seconds (Acceleration of 5m/s2
means that the velocity is
increasing by 5m/s every second
for 6 seconds where the velocity
reached will be 5m/s × 6 =
30m/s).
Gradient
of
OA
represents the acceleration
(Acceleration = Velocity ÷ Time
or Change in y value ÷ Change in
x value).
2. From A to B, the car is moving at
constant velocity (i.e. 30m/s
where gradient of AB is zero and
therefore, no acceleration)
3. From B to C down to the time axis, where C is 3 units down the velocity axis (i.e. 3m/s)
and 1 unit along the time axis (i.e. 1 sec) from B. Thus, a deceleration of 3m/s2 (Gradient
of BC is -3, that is, a deceleration of 3m/s2).
Examples on Velocity Time Graphs
1. The velocity-time graph illustrates the journey of a car between a set of traffic-lights and
a zebra crossing.
a)
b)
c)
d)
e)
f)
What is the car’s acceleration for the first 4 seconds?
What happens when t = 4?
For how long is the car moving at a constant velocity?
For how long is the car braking?
What is the deceleration of the car?
For how long is the car moving?
2. The velocity-time graph illustrates the first 7 minutes of the flight of a rocket.
a)
b)
c)
d)
What is the initial acceleration of the rocket?
What is the velocity of the rocket 2 minutes after its launch?
What is the steady velocity obtained by the rocket?
What is the acceleration of the rocket during the fourth minute of its flight?
3. This velocity-time graph illustrates the journey of a train between two stations.
a)
b)
c)
d)
e)
What is the acceleration for the first 2 minutes in km/h2?
What is the greatest velocity of the train?
For how long is the train travelling at constant velocity?
What is the acceleration during the third minute km/h2?
What is the deceleration of the train km/h2?
For question 4 to 6, draw a velocity-time graph to illustrate the following journeys. Use 1cm
for 1 second and 2cm for 5m/s.
4. A car accelerates steadily from rest reaching a velocity of 12m/s in 10 seconds.
5. A train accelerates from rest reaching a velocity of 8m/s in 5 seconds and then
immediately decelerates to rest in 4 seconds.
6. A motor bike accelerates from rest to a velocity of 20m/s in 4 seconds, maintains this
steady velocity for 8 seconds and then decelerates to rest in 5seconds.