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Question

The position of a particle is given by r=3t^i+3t2^j4^k where t is in seconds and r is meters. Find out magnitude of velocity v and angle made by velocity v with X-axis at t=3 s.

A
35 m/s,θ=tan1(2)
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B
35 m/s, θ=tan1(23)
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C
32 m/s,θ=tan1(3)
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D
35 m/s, θ=tan1(12)
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Solution

The correct option is A 35 m/s,θ=tan1(2)
It is given that the position vector r=3t^i+3t2^j4^k.

We know that velocity is derivative of position with respect to time,

v=drdt=3^i+23t^jv(t=3s)=3^i+6^j|v|=32+62=35 m/sθ=tan1(63)=tan1(2)

Hence option A is the correct answer.

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