Consider a body of mass 1.0 kg at rest at the origin at time

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

t=0

. A force

\vec{F} = (\alpha t \hat{i} + \beta \hat{j})

is applied on the body, where

\alpha = 1.0 \text{ Ns}^{-1}

and

\beta = 1.0 \text{ N}

. The torque acting on the body about the origin at time

t = 1.0 \text{ s}

\vec{\tau}

. Which of the following statements is (are) true? [Adv. 2018] (1)

|\vec{\tau}| = \frac{1}{3} \text{ Nm}

(2) The torque

\vec{\tau}

is in the direction of the unit vector

+\hat{k}

(3) The velocity of the body at

t = 1 \text{ s}

\vec{v} = \frac{1}{2}(\hat{i} + 2\hat{j}) \text{ ms}^{-1}

(4) The magnitude of displacement of the body at

t = 1 \text{ s}

\frac{1}{6} \text{ m}