A particle moves along positive branch of the curve, `y = x/2, where x = t^3/3`, x and y are measured in meters and t in seconds, then

Options

A. The velocity of particle at `t = 1 s is hati + 1/2 hatj`.
B. The velocity of particle at `t = 1 s is 1/2 hati + hatj`.
C. The acceleration of particle at ` t= 2 s is 2hati+hatj`.
D. The acceleration of particle at ` t= 2 s is hati+ 2hatj`.

Answer

A, C

Explanation

a,c. `(dx)/(dt) = t^2` ……………..(i)
`y = 1/2 t^3/3 rArr (dy)/(dt) = t^2/2`…………..(ii)
`t = 1, v_x = 1, v_y = 1/2 rArr vecv = hati + 1/2 hatj`.
`(d^2x)/(dt^2)= 2t` ………(iii)
`(d^2y)/(dt^2) = t` ……(iv)
At t = 1 s, `a_x = 2 and a_y = 1`
`rArr veca = 2hati + hatj`.