Free Printable Motion and Rates

1.

A stone is thrown upwards and then falls back onto the ground.

Which of the following is true at the top of its flight?

a)

Neither the velocity nor the acceleration is zero.

b)

Both the velocity and the acceleration is zero.

c)

The acceleration is zero, but the velocity is not zero.

d)

The velocity is zero, but the acceleration is not zero.

2.

A truck took one hour to travel south 60 km, then took two hours to travel north 100 km, then took another two hours to travel south 120 km.

What was the average speed at which the truck was travelling over these five hours?

a)

$56$ km/h

b)

$16$ km/h

c)

$56\frac{2}{3}$ km/h

d)

The average speed cannot be determined from this data.

3.

A particle moves according to the equation $x=t^3-6t^2+5t-20.$

Which of the following statements is true when 𝑡 = 3?

a)

The velocity is positive and the acceleration is positive.

b)

The velocity is negative and the acceleration is positive.

c)

The velocity is positive and the acceleration is negative.

d)

The velocity is negative and the acceleration is negative.

4.

A particle is moving according to the equation $x=6-12\cos\frac{\pi t}{12}.$

At which of the following times is the particle’s velocity neither increasing nor decreasing?

a)

$t=0$

b)

$t=4$

c)

$t=12$

d)

$t=18$

5.

A particle moves according to the equation $x=t^4-4t^3.$

At what time is the acceleration of the particle minimum?

a)

$t=1$

b)

$t=2$

c)

$t=3$

d)

$t=4$

6.

A particle is moving with acceleration 𝑥̈ = $6e^{-3t}\ ,$ in units of metres and seconds. Initially its velocity is 3 metres per second and its displacement is −3 metres.

What is the formula for its displacement in terms of time 𝑡?

a)

$x=\frac{2}{3}e^{-3t}+t-3\frac{1}{3}$

b)

$x=\frac{2}{3}e^{-3t}+t-2\frac{1}{3}$

c)

$x=\frac{2}{3}e^{-3t}+5t-3\frac{2}{3}$

d)

$x=\frac{2}{3}e^{-3t}+5t-2\frac{1}{3}$

7.

The acceleration of a particle is given by 𝑥̈ = 40 cos 2𝑡, in units of metres and seconds. At time zero, the displacement and the velocity are both zero. At which of the following times is the particle 5 metres on the positive side of the origin?

a)

$t=\frac{\pi}{3}$

b)

$t=\frac{3\pi}{2}$

c)

$t=\frac{3\pi}{4}$

d)

$t=\frac{5\pi}{6}$

8.

The population 𝑃 of a town has been increasing since the start of 2015 according to the equation $P=5238e^{0.07t}\ ,$ where 𝑡 is in years.

At what rate, in people per annum, was the population increasing at the start of 2019?

a)

6030

b)

6931

c)

485

d)

452

9.

Liquid is leaking out of a large storage tank at the rate of 𝑅 litres per day according to the equation $R=100+\frac{500}{1+t}.$

How much liquid, correct to the nearest litre, has leaked from the tank in the first week?

a)

1140 litres

b)

1740 litres

c)

163 litres

d)

1673 litres

10.

The sides of a square have length 𝑥 metres and are increasing at a rate of 0.2 m/s. When the side of the square is 4 metres long, at what rate is the area of the square increasing?

a)

0.8 m²/s

b)

1.2 m²/s

c)

1.6 m²/s

d)

2.4 m²/s

11.

A particle is moving along a straight line. The graph shows the acceleration of the particle.

For what value of t is the velocity v a maximum?

a)

1

b)

2

c)

3

d)

4

e)

5

12.

A particle is moving along a straight line with displacement x at time t.

The particle is stationary when t = 11 and when t = 13.

Which of the following MUST be true in this case?

a)

The particle changes direction at some time between t = 11 and t = 13.

b)

The displacement function of the particle has a stationary point at some time

between t = 11 and t = 13.

c)

The acceleration of the particle is 0 at some time between t = 11 and t = 13.

d)

The acceleration function of the particle has a stationary point at some time between t = 11 and t = 13.

13.

A particle is moving along a straight line. The graph shows the velocity, v, of the particle for time t ≥ 0.

How many times does the particle change direction?

a)

1

b)

2

c)

3

d)

4

14.

A particle is moving along the x-axis. The graph shows its velocity v metres per second at time t seconds.

When t = 0 the displacement x is equal to 2 metres. What is the maximum value of the displacement x?

a)

8 m

b)

14 m

c)

16 m

d)

18 m

15.

The graph shows the displacement x of a particle moving along a straight line as a function of time t.

Which statement describes the motion of the particle at the point P?

a)

The velocity is negative and the acceleration is positive.

b)

The velocity is negative and the acceleration is negative.

c)

The velocity is positive and the acceleration is positive.

d)

The velocity is positive and the acceleration is negative.

Motion and Rates

Total questions: 15

Worksheet time: 29mins

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