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Question

A particle is moving along a circular path of radius 0.7m with tangential acceleration of 5ms-2 The particle is initially at rest.
Based on above information, answer the following question:
1.The speed of the particle after 7s is


A

5ms-1

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B

7ms-1

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C

35ms-1

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D

48ms-1

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Solution

The correct option is C

35ms-1


Step 1: Given data:

Tangential acceleration and radius :aT=5ms-2,R=0.7m

Formula used:

Tangential acceleration: aT=Rα where α is the angular acceleration.

By equation of motion, ω=ω0+αt where ω0is the initial angular velocity and ωis the final angular velocity.

Relation between linear and angular velocity ν=Rω where R is the radius.

Step 2: To find tangential acceleration:

α=aTRα=50.7α=7.143rads-2

Step 3: To find angular velocity:

We know ω=ω0+αt where ω0is the initial angular velocity and ωis the final angular velocity.

Buthereω0=0ω=αtω=7.143×7[t=7s]ω=50rads-1

Step 4: To find the linear speed:

We know that the linear speed is given as
ν=Rων=0.7×50ν=35ms-1

The speed of the particle after 7s is 35ms-1.

Hence, option (c) is correct.


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