A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by x( t)=alpha t^2+beta t+gamma m, where alpha=1 m / s^2, beta=1 m / s and gamma=1 m. The work done on the body during the time interval t=2 s to t=3 s, is\ \_\_\_\_ J.

x( t)= t^2+ t+1 v( t)=2 t+1 a( t)=2 F=4 N. Displacement = x(3)- x(2) =13-7=6 M W= F . S=4 x 6=24 J

A body of mass 2 kg is moving along x direction such th... | null (Physics) | DivineJEE

JEE Mains 2026 21st January Shift 2

Physics

A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by

\mathrm{x}(\mathrm{t})=\alpha \mathrm{t}^{2}+\beta \mathrm{t}+\gamma \mathrm{m}

, where

\alpha=1 \mathrm{~m} / \mathrm{s}^{2}

\beta=1 \mathrm{~m} / \mathrm{s}

and

\gamma=1 \mathrm{~m}

. The work done on the body during the time interval

\mathrm{t}=2 \mathrm{~s}

\mathrm{t}=3 \mathrm{~s}

, is\\

\_\_\_\_

Correct Answer:

\mathrm{x}(\mathrm{t})=\mathrm{t}^{2}+\mathrm{t}+1\\

\mathrm{v}(\mathrm{t})=2 \mathrm{t}+1\\

\mathrm{a}(\mathrm{t})=2\\

\mathrm{F}=4 \mathrm{~N}.\\

Displacement

=\mathrm{x}(3)-\mathrm{x}(2)\\

=13-7=6 \mathrm{M}\\

\mathrm{W}=\mathrm{F} . \mathrm{S}=4 \times 6=24 \mathrm{~J}

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