MEDIUM

AS and A Level

IMPORTANT

Earn 100

A van driver wants to pull out from rest onto a road where cars are moving at a constant speed of $20 m s^{- 1} .$ When there is a large enough gap between cars, the van driver pulls out immediately after one car passes. She then accelerates at a constant rate of $4 m s^{- 2}$ until moving at $20 m s^{- 1} .$ To do this safely the car behind must always be at least $10 m$ away. Find the minimum length of the gap between the cars for the van driver to pull out.

Important Questions on Velocity and Acceleration

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1D>Q 12

A police motorcyclist is stationary when a car passes, driving dangerously at a constant speed of

40 m s^{- 1} .

At the instant the car passes, the motorcyclist gives chase, accelerating at

2.5 m s^{- 2}

until reaching a speed of

50 m s^{- 1}

before continuing at a constant speed. Show that the motorcyclist has not caught the car by the time he reaches top speed. Find how long after the car initially passed him the motorcyclist catches up to the car.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1D>Q 13

The front of a big wave is approaching a beach at a constant speed of

11.6 {ms}^{- 1} .

When it is

30 m

away from a boy on the beach, the wave starts decelerating at a constant rate of

1.6 m s^{- 2}

and the boy walks away from the sea at a constant speed of

2 m s^{- 1} .

Show that the wave will not reach the boy and find the minimum distance between the boy and the wave.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1D>Q 14

Swimmers going down a waterslide

30 m

long push themselves off with an initial speed of between

1 m s^{- 1}

and

2 m s^{- 1} .

They accelerate down with constant acceleration

0.8 m s^{- 2}

for the first

20 m

before more water is added and the acceleration is

1 m s^{- 2}

for the last

10 m

of the slide. For safety there must be at least

5 s

between swimmers arriving at the bottom of the slide. Find the minimum whole number of seconds between swimmers being allowed to start the slide.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1D>Q 15

A ball is projected in the air with initial speed

u

and goes up and down with acceleration

g

downwards. A timer is at a height

h

. It records the time from the ball being projected until it passes the timer on the way up as

t_{1}

and on the way down as

t_{2}

. Show that the total of the two times is independent of

h

and that the initial speed can be calculated as

u = \frac{g (t_{1} + t_{2})}{2}

. Show also that the difference between the times is given by

\frac{2 \sqrt{u^{2} - 2 g h}}{g}

. Hence, find a formula for

h

in terms of

t_{1,} t_{2}

and

g

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 1

A ball is projected in the air with initial speed

u

and goes up and down with acceleration

g

downwards. A timer is at a height

h .

It records the time from the ball being projected until it passes the timer on the way up as

t_{1}

and on the way down as

t_{2} .

Show that the total of the two times is independent of

h

and that the initial speed can be calculated as

u = \frac{g (t_{1} + t_{2})}{2} .

Show also that the difference between the times is given by

\frac{2 \sqrt{u^{2} - 2 g h}}{g} .

Hence, find a formula for

h

in terms of

t_{1}, t_{2}

and

g .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 1

Rinesh starts from rest, moving north with a constant acceleration of $3 m s^{- 2}$ for $5 s .$ Sketch the velocity-time graphs from the information given. Take north to be the positive direction.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 1

Wendi is moving north at $2 m s^{- 1}$ when she starts to accelerate at a constant rate of $0.5 m s^{- 2}$ for $6 s .$ Sketch the velocity-time graphs from the information given. Take north to be the positive direction.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1E>Q 1

Dylon is moving south at a constant speed of $4 m s^{- 1} .$ Sketch the velocity-time graph from the information given. Take north to be the positive direction.

Important Questions on Velocity and Acceleration

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