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The co-ordinates of a moving particle at...

The co-ordinates of a moving particle at anytime '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

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

C

` 3 t^(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 = alpha t^(2) and y = beta t^(3)`
`rArr v_(x) = (dx)/( dt) v _(y) = (dy)/( dt) = 3 beta t^(2)`
`= 3 alpha t^(2)`
` v = sqrt( v_(x)^(2) + v_( y)^(2)) = 3 t ^(2) sqrt( alpha ^(2) + beta^(2))`
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