Booklet 1A - Dynamics (Worked Examples)

Question 1

Example

At the 2008 Beijing Olympics, Usain Bolt ran 100m in 9.69 seconds. Calculate his average speed.

Answer 1

d = 100 m
t = 9.69 s
v = ?

d = v t
100 = v x 9.69
v x 9.69 = 100
v = 100/9.69
v = 10.32 ms^-1

Question 2

Example of how to work out average speed and average velocity using scale diagram or calculation:

A walker travels 12km South then 5km West in 4 hours. Calculate:

a) the distance travelled
b) the resultant displacement
c) the average speed
d) the average velocity

(See Image)

Answer 2

a) d = 12 + 5 = 17 km

b) a² = b² + c²
a² = 5² + 12² = 25 + 144 = 169
a = sqrt(169) = 13 km
tan(x) = Opp/Adj = 5/12
x = tan^-1(5/12) = 23º
Bearing is clockwise from North i.e. 180 + 23 = 203º
Resultant Displacement is 13 km bearing 203º

c) d = 17 km; t = 4 h; v = ?
d = vt
17 = v x 4
v x 4 = 17
v = 17/4 = 4.25 kmh^-1

d) s = 13 km (207º); t = 4 h; v = ?
s = vt
13 = v x 4
v x 4 = 13
v = 13/4 = 3.25 kmh^-1 (207º)

Question 3

An arrow is fired vertically upwards. It reaches a maximum height of 65m.

a. State the velocity of the arrow at its maximum height?
b. Calculate the initial velocity of the arrow.

Answer 3

Question 4

Interpret displacement-time graphs.

Answer 4

Question 5

Answer 5

Question 6

Interpret velocity-time graphs.

Answer 6

Question 7

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Question 8

Answer 8

Question 9

a. Draw a free body diagram for a skydiver accelerating after they jump out of an aeroplane using a drogue chute to slow their descent.
b. Find an expression for the unbalanced force on the skydiver.

Answer 9

Question 10

A load of bricks of mass 1000kg is being lifted by a crane at constant speed. Calculate the tension in the crane cable.

Answer 10

Question 11

A cyclist of mass 100kg is accelerating at 1.0ms^-2 along a level road. The total frictional force due to air resistance and rolling resistance is 20N. Calculate the forward force produced by the cyclist.

Answer 11

Question 12

A rocket of mass 1000kg produces a constant thrust of 20,000N.

Calculate its acceleration.

Answer 12

Question 13

A 60kg student is standing in a lift of mass 200kg. Calculate the tension in the lift cable when

a. the lift is stationary
b. the lift is moving downwards at a constant speed.
c. the lift is moving downwards and decelerating at 1.0ms^-2.

Answer 13

Question 14

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Question 15

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Question 16

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Question 17

A boy on a sledge of total mass of 55kg is sliding down a 20° slope. The sledge accelerates at 3.0ms-². Find the frictional force on the sledge.

Answer 17

Question 18

Answer 18

The final answer should be 5.9 m/s

Question 19

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Question 20

Answer 20

Question 21

A 45g golf ball is struck with a club with an average force of 3800N and moves off with a velocity of 45ms^-1. For how long was the ball in contact with the club.

Answer 21

Question 22

Answer 22