Chapter 16 - Rates of Change

A bushwalker in South Australia walks 10km in 2 hours, stops for 30 minutes and then walks a further 8km in another 2 hours. The average walking speed of the bushwalker over the entire walk is:

• 4.5km/h

• 9km/h

• 5km/h

• 4km/h

• 7.2km/h

A 200 litre water tank is emptied. If it takes 4.5 hours to empty the tank, assuming a constant rate of flow, the rate of flow at which the tanks is emptied is:

• 2.25 litres/hour

• 44.44 litres/hour

• 4.44 litres/hour

• 50 litres/hour

• 1.35 litres/hour

The average rate of change of the function y = 2 x 3^x over the interval [0, 4] is:

• 44

• 162

• 158

• 40

• 4

The average rate of change of the function y = 5 + 7x - 3x² over the interval [0, 0.01] is calculated to be 6.97. From this we can estimate that at x = 0, the instanteous rate of change of y = 5 +7x - 3x² is approximately:

• 0.7

• 0

• 0.07

• 7

• impossible to estimate

The distance-time graph shows the movement of a train over a period of time. For the section of graph between O and A, the train is:

• speeding up

• slowing down

• travelling north

• travelling at a constant speed

• stationary

The distance-time graph shows the movement of a train over a period of time. For the section of the graph between A and B, the train is:

• speeding up

• slowing down

• travelling east

• travelling at a constant speed greater than zero

• stationary

The distance-time graph shows the movement of a train over a period of time. The train is stationary corresponding to the parts of the graph

• at O and E

• between A and B only

• between C and D only

• between A and B, C and D

• never

The distance-time graph shows the movement of a train over a period of time. The train is travelling fastest for the section of the graph between:

• O and A

• A and B

• B and C

• C and D

• D and E

The distance-time graph shows the movement of a train over a period of time. If E is 75km from O and the train arrives at E 55 minutes after leaving O, the average speed of the train over the entire journey is closest to

• 1.36 km/min

• 1.36 km/h

• 0.73 km/min

• 75 km/h

• 55 km/h

At 0 seconds, Mr Soumalias was 10 metres off the ground. At 5 seconds, he was 30 metres off the ground. What is his rate in metres per second?

• 10 m per second

• 5 m per second

• 4 m per second

• 6 m per second

• 2 m per second