1. Dynamics and Space Learning Intention You will be able to:
Carry out calculations using the relationship between time, change of speed and acceleration.

2. Acceleration = change in speed time for the speed to change
a = v – u u is the initial (starting) speed in metres per second(m/s) t
v is the final speed in metres per second (m/s)
t is the time between these two speeds in seconds (s)
a is the acceleration in metres per second per second (m/s2)
Always substitute values into the formula. Never Never rearrange the symbols.
Always rearrange the values. You will lose less marks this way if you make a mistake

3. Calculate the change in speed of the car and then its acceleration.
How fast in what time?

4. Example
A car speeds up from 12 m/s to 26 m/s in 7s.
Calculate the acceleration.
a = v – u t
a = 26 – 12 7
= 14
= 2m/s2 a=
u= 12m/s
v= 26m/s
t= 7s

5. 1 A cyclist accelerates from rest to a speed of 12 m/s in 8 s
1 A cyclist accelerates from rest to a speed of 12 m/s in 8 s Calculate his acceleration.

6. 2 A free-fall parachutist accelerates from rest to 45 m/s in 4. 5 s
2 A free-fall parachutist accelerates from rest to 45 m/s in 4.5 s. Calculate her acceleration.

7. 3 A car is travelling at 20 m/s on a motorway.
It accelerates at 2.5 m/s2 for 6 s.
Calculate the final speed of the car.

8. 4 A train travelling at 40 m/s applies the breaks and reduces its speed to 13 m/s in 18 s.
Calculate the train’s acceleration.
What is special about the answer?
Can you explain why this happens?

9. 5 Two cars accelerate from rest.
A blue one at 2 m/s2 for 15 seconds. A red one at 3 m/s2 for 9 seconds.
Which one has the higher final speed? (show all your working).

10. A glider cruising at 20 m/s goes into a dive and accelerates at 4 m/s2 for 8 seconds and then levels out. What final speed does it reach?

11. 7 A lorry travelling at a constant speed begins to accelerate at 1
7 A lorry travelling at a constant speed begins to accelerate at 1.5 m/s2 for 6 seconds by which time it has reached a speed of 20 m/s. What was its original speed?

12. 8 A train decelerates at the rate of 1
8 A train decelerates at the rate of 1.5 m/s2 from a speed of 30 m/s for 20 seconds.
What is its speed at the end of the 20 seconds?

13. The following table shows some performance figures for cars.
Calculate the biggest acceleration shown in the table.
Which car is it?
Calculate the smallest acceleration shown in the table.
How could you tell which is the biggest and smallest accelerations without calculating the figures?
Explain your answer fully.
Car
Top speed
(m/s)
Time for 0-27 m/s
(s)
Arial Atom V8 76
2.3
SSC Ultimate Aero TT
122
2.8
BMW M5 F10 69
4.4
Ford Mondeo ST24 59
8.0
Volvo XC60 58
7.1
Formula 1 car
103
1.7

14. 2000 SQA General Q13.
A group of students is using the apparatus shown to study the motion of a trolley. The trolley is released from rest at the top of the slope. The stopwatch measures the time taken for the trolley to reach the light gate.
(a) Describe how to find the instantaneous speed of the trolley as it passes through the light gate.
You must state the measurements that are made and how they are used.
(b) During one run, the instantaneous speed of the trolley through the light gate is calculated to be 0.8 metres per second. The stopwatch reading is 2.0 seconds.
Calculate the acceleration of the trolley down the slope.
(c) The light gate is moved closer to the top of the slope and the experiment is repeated.
One student suggests that the value of acceleration obtained is more accurate, because the reading on the stopwatch is less.
Explain whether the student is correct or not.