An exercise routine involves a mixture of jogging at 4 m s - 1 and sprinting at 7 m s - 1 . An athlete covers 1 km in 3 minutes and 10 seconds. Find how long she spent sprinting.

The time taken by athlete to cover 1 km is 3 min 10 s = 190 s . Assuming time taken for jogging is t . The taken for sprinting will be 190 s - t . The total distance covered is 1000 m . Thus, 1000 m = v 1 t + v 2 190 s - t So, we get, t = 110 s . Thus, the time taken for sprinting is 190 s - 110 s = 80 s Hence, the time of sprinting is 80 s .

A car accelerates from 4 m s - 1 to 10 m s - 1 in 3 s at constant acceleration. Find its acceleration.

Given, Final velocity, v = 10 m s - 1 Initial velocity, u = 10 m s - 1 Time taken, t = 3 s For an object moving at constant acceleration, acceleration = change in velocity time taken Let a be the acceleration, then, a = v - u t where v is final acceleration, u is initial acceleration and t is time taken. Substituting the values, we get, a = 10 - 4 3 = 6 3 = 2 m s - 2 . So, the required acceleration is 2 m s - 2 .

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The speed of sound in wood is $3300 m s^{- 1}$ and the speed of sound in air is $330 m s^{- 1} .$ A hammer hits one end of a $33 m$ long plank of wood. Find the difference in time between the sound waves being detected at the other end of the plank and the sound being heard through the air.

Important Questions on Velocity and Acceleration

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1A>Q 10

An exercise routine involves a mixture of jogging at

4 m s^{- 1}

and sprinting at

7 m s^{- 1} .

An athlete covers

1 km

3

minutes and

10

seconds. Find how long she spent sprinting.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1A>Q 11

Two cars are racing over the same distance. They start at the same time, but one finishes

8 s

before the other. The faster one averaged

45 m s^{- 1}

and the slower one averaged

44 m s^{- 1} .

Find the length of the race.

MEDIUM

AS and A Level

IMPORTANT

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

Two air hockey pucks are

2 m

apart. One is struck and moves directly towards the other at

1.3 m s^{- 1} .

The other is struck

0.2 s

later and moves directly towards the first at

1.7 m s^{- 1} .

Find how far the first puck has moved when the collision occurs and how long it has been moving for.

MEDIUM

AS and A Level

IMPORTANT

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

A motion from point $A$ to point $C$ is split into two parts. The motion from $A$ to $B$ has displacement $s_{1}$ and takes time $t_{1} .$ The motion from $B$ to $C$ has displacement $s_{2}$ and takes time $t_{2} .$

Prove that if $t_{1} = t_{2},$ the average speed from $A$ to $C$ is the same as the average of the speeds from $A$ to $B$ and from $B$ to $C .$

MEDIUM

AS and A Level

IMPORTANT

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

Prove that if $s_{1} = s_{2},$ the average speed from $A$ to $C$ is the same as the average of the speeds from $A$ to $B$ and from $B$ to $C$ if, and only if, $t_{1} = t_{2} .$

MEDIUM

AS and A Level

IMPORTANT

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

The distance from point $A$ to point $B$ is $s .$ In the motion from $A$ to $B$ and back, the speed for the first part of the motion is $v_{1}$ and the speed for the return part of the motion is $v_{2} .$ The average speed for the entire motion is $v .$

Prove that $v = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}} .$

MEDIUM

AS and A Level

IMPORTANT

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

Deduce that it is impossible to average twice the speed of the first part of the motion; that is, it is impossible to have $v = 2 v_{1} .$

EASY

AS and A Level

IMPORTANT

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

A car accelerates from

4 m s^{- 1}

10 m s^{- 1}

3 s

at constant acceleration. Find its acceleration.

The speed of sound in wood is 3300 m s-1 and the speed of sound in air is 330 m s-1. A hammer hits one end of a 33 m long plank of wood. Find the difference in time between the sound waves being detected at the other end of the plank and the sound being heard through the air.

Important Questions on Velocity and Acceleration

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The speed of sound in wood is $3300 m s^{- 1}$ and the speed of sound in air is $330 m s^{- 1} .$ A hammer hits one end of a $33 m$ long plank of wood. Find the difference in time between the sound waves being detected at the other end of the plank and the sound being heard through the air.