A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by x(t) = αt² + βt + γm, where α = 1 m/s², β = 1 m/s and γ = 1m. The work done on the body during the time interval t = 2 s to t = 3 s, i $s ________$ J.
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Question

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by x(t) = αt² + βt + γm, where α = 1 m/s², β = 1 m/s and γ = 1m. The work done on the body during the time interval t = 2 s to t = 3 s, i $s ________$ J.

Options

G1 Physics · Accepted Answer

Using the given constants, x(t) = t² + t + 1. Velocity is v(t) = dx/dt = 2t + 1. Acceleration is a(t) = dv/dt = 2 m/s². Therefore the force is F = ma = 2 × 2 = 4 N. The displacement from t = 2 s to t = 3 s is Δx = x(3) - x(2) = (9 + 3 + 1) - (4 + 2 + 1) = 13 - 7 = 6 m. Hence the work done is W = FΔx = 4 × 6 = 24 J. Correct option: C.

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by x(t) = αt² + βt + γm, where α = 1 m/s², β = 1 m/s and γ = 1m. The work done on the body during the time interval t = 2 s to t = 3 s, i s ________ J.