A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by x(t) = α t² + β t + γ m, where α = 1 m/s², β = 1 m/s and γ = 1 m. The work done on the body during the time interval t = 2 s to t = 3 s, is ________ J. (a) 42 (b) 24 (c) 49 (d) 12

Answer: (b). v = dx/dt = 2α t + β = 2t + 1 v(2) = 5 m/s, v(3) = 7 m/s W = 1/2(2)(7² - 5²) = 49 - 25 = 24 J So the answer is (b) 24.

A body of mass 2 kg is moving along x-direction such that its… | JEE Main 2026 (21 Jan, Shift 2)

Q3JEE Main 2026 · 21 JAN · SHIFT 2Medium

Work-Energy Theorem

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 $\alpha = 1\text{ m/s}^2, \beta = 1\text{ m/s}$ and $\gamma = 1\text{ m}$ . The work done on the body during the time interval $t = 2\text{ s}$ to $t = 3\text{ s}$ , is ________ J.

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Answer: (b)

$v = \frac{dx}{dt} = 2\alpha t + \beta = 2t + 1$
$v(2) = 5\text{ m/s}$ , $v(3) = 7\text{ m/s}$
$W = \frac{1}{2}(2)(7^2 - 5^2) = 49 - 25 = 24\text{ J}$
So the answer is (b) 24.

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