Consider a body of mass 1.0 at rest at the origin at time `t = 0`. A force `vec F=(alpha t hat l +beta hat J) ` is applied on the body, where `alpha =1.0 Ns^(-1) and beta =1.0 N`. The torque acting on the body about the origin at time `t=1.0 s " is " vec tau` . Which of the following statements is (are) true?

Options

A. |r|=1/3 Nm`
B. `The torque `vectau` is in the direction of the unit vector `-hatk`
C. The velocity of the body at `t=1s` is `vecv =1/2 (hati + 2hatj)ms^(-1)`
D. The magnitude of displacement of the body at t=1s is `1/6` m

Answer

A, C

Explanation

`veca = thati + hatj m//s^(2)`
`rArr vecv = t^(2)/2 hati + thatj m//s rArr vecr =t^(3)/6 hati + t^(2)/2 hatj m`
So, `vectau = vecr xx vecF =(t^(3)/2 - t^(3)/6) (-hatk) = t^(3)/3 (-hatk) Nm`