Question

A particle moves along the curve `y = x^2 /2.` Here x varies with time as `x = t^2 /2.` Where x and y are measured in metres and t in seconds. At `t = 2 s,` the velocity of the particle (in `ms^-1`) is
A. `4 hat i + 6 hat j`
B. `2 hat i + 4 hat j`
C. `4 hat i + 2 hat j`
D. `4 hat i + 4 hat j`

Answer 1

Correct Answer - B
`x=(t^2)/2`
`:. v_x=(dx)/(dt)=t y=x^2/2=t^4/8`
`:. v_y=(dy)/(dt)=t^3/2`
At `t=2s`
`v_x=2m//s`
and `v_y=4m//s`
`:. v=v_x hati+v_y hatj=(2 hati+4 hatj) m//s`