Question

The distance traveled by an object along the axes are even by ` x= 2 t^2 , y=t^2-4 t, z=3 t -5`. The initial velocity of the particle is .
A. (a) ` 10 unit`
B. (b) ` 12 unit`
C. (c ) ` 5 unit `
D. (d) ` 2 unit`

Answer 1

Correct Answer - C
Given, ` s= 2 t^2` so (dx)/(dt) =4 t`
y= t^2 -4 t so ` (dy)/(dt) = 2 t-4`
` z=3 t- 5 `so ` (dz)/(dt) =3`
velocity `, vec v = (dx)/(dt) hat + (dy)/(dt) hat j + (dz)/(dt) hat k`
` = 4 t hat I + ( 2 t- 4) hat j + 3 hat k`
When ` t=0, vec v=- 4 hat j + 3 hat k`
so ` v= sqrt (9-4)^2 + (3)^2) = 5 unit` .