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 .

A car accelerates from rest to 10 m s - 2 in 4 s at constant acceleration. Find its acceleration.

Given, Final velocity, v = 10 m s - 1 Initial velocity, u = 0 m s - 1 ( As the body accelerates from rest. ) Time taken, t = 4 s For an object moving at constant acceleration, acceleration = change in velocity time taken Let a be the acceleration, then, a = v - u t Substituting the values, we get, a = 10 - 0 4 = 10 4 = 2 . 5 m s - 2 . So, the required acceleration is 2 . 5 m s - 2 .

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AS and A Level

IMPORTANT

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

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 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 $v .$

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.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1B>Q 2

A car accelerates from rest to

10 m s^{- 2}

4 s

at constant acceleration. Find its acceleration.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1B>Q 3

A car accelerates from

3 m s^{- 1}

at an acceleration of

6 m s^{- 2}

. Find the time taken to reach

12 m s^{- 1}

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1B>Q 4

An aeroplane accelerates at a constant rate of

3 m s^{- 2}

for

5 s

from an initial velocity of

4 m s^{- 1}

. Find its final velocity.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1B>Q 5

A speedboat accelerates at a constant rate of

1.5 m s^{- 2}

for

4 s

, reaching a final velocity of

9 m s^{- 1}

. Find its initial velocity.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1B>Q 6

A car decelerates at a constant rate of

2 m s^{- 2}

for

3 s

, finishing at a velocity of

8 m s^{- 1}

. Find its initial velocity.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 1 - Velocity and Acceleration>EXERCISE 1B>Q 7

A car accelerates from an initial velocity of

4 m s^{- 1}

to a final velocity of

8 m s^{- 1}

at a constant rate of

0.5 m s^{- 2}

. Find the car

'

s displacement in that time.

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 v1 and the speed for the return part of the motion is v2. The average speed for the entire motion is v. Prove that v=2v1v2v1+v2.

Important Questions on Velocity and Acceleration

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