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

Options

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)`

Answer

B

Explanation

As `x = alpha t^3 and y = betat^3`
`:. v_x =(dx)/(dt) = 3 alphat^2 and v_y=(dy)/(dt) = 3betat^2`
`:. v^2 =v_x^2+v_y^2=(3alphat^2)^2+(3betat^2)^2=(3t^2)^2(alpha^2+beta^2)`
or `v = 3t^2sqrt(alpha^2+beta^2)`