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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

`3tsqrt(alpha^(2) +beta^(2))`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`x = alphat^(3), y = betat^(3)`
`V_(x) = (dx)/(dt) = 3 alphat^(2)`
`V_(y) = (dy)/(dt) = 3betat^(2)`
Resultant velocity
`V = sqrt(v_(x)^(2) +v_(y)^(2))`
`= sqrt(9alpha^(2)t^(4) + 9 beta^(2)t^(4))`
`= 3t^(2) sqrt(alpha^(2) +beta^(2))`
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