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The coordinates of a moving particle at ...

The coordinates of a moving particle at any time `t` are given by `x = alpha t^(3)` and `y = beta t^(3)`. The speed of the particle at time `t` is given by

A

` sqrt ( alpha ^ 2 + beta ^ 2 ) `

B

`3t sqrt ( alpha ^ 2 + beta ^2 ) `

C

`3t^ 2 sqrt ( alpha ^ 2 + beta ^ 2 ) `

D

`t ^ 2 sqrt ( alpha ^ 2 + beta ^ 2 ) `

Text Solution

Verified by Experts

The correct Answer is:
C
`x=alphat^(2) and y=beta t^(3)`
x-component of the velocity : `v_(x)=(dx)/(dt)=3alpha t^(2)` and y-component of the velocity `v_(y)=(dy)/(dt)=3beta t^(2)`
Resultant velocity `v=sqrt(v_(x)^(2)+v_(y)^(2))=3t^(2) sqrt(alpha^(2)+beta^(2))`
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