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Question

The co-ordinates of a moving particle are x=at2 and y=bt2, where a and b are constants. the velocity of a particle at any instant is


A

2ta2++b2

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B

2ta+b

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C

2ta2+b2

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D

a2+b2

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Solution

The correct option is C

2ta2+b2


Step 1. Given data

x=at2,

y=bt2

Step 2. Formula to be used.

Particle velocity is the velocity of a particle in a medium as it transmits a wave is called as the velocity of the particle.

The velocity of particle is,

v=vx2+vy2

Step 3. Find the velocity of the particle.

The velocity of the particle is,

vx=dxdt

=2at

vy=dydt

=2bt

So,

v=4a2t2+4b2t2

=2ta2+b2

So, the velocity of the particle is 2ta2+b2.

Hence, option C is the correct answer.


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