Question

A body with mass 5 kg is acted upon by a force `vec(F) = (- 3 hat (i) + 4 hat (j)) N`. If its initial velocity at t =0 is `vec(v) = 6 hat(i) - 12 hat (j) ms^(-1)`, the time at which it will just have a velocity along the y-axis is :

Answer 1

Correct Answer - B
Here, `m=5kg, bar(F)=-3hati-4 hatjN`
`bar(u)=6hati-12hatj ms^(-1)`
The acceleration of the body is
`=bar(a)=(bar(F))/(m)=(-3hati+4hatjN)/(5kg)=(3)/(5)hati+(4)/(5)hatj ms^(-2)`
Velocity of the body alon x-axis at any time t si
`v_(x)=u_(x)+a_(x)t=6-(3)/(5)t`
As the body will have velocity along y-axis, therefore is velocity along x-axis will be zero.
`i.e. v_(x)=0 or 6=(3)/(5)t Rightarrow t=(30)/(3)=10s`