A body of mass 2kg is moving along x-direction such that its displacement as function of time is given by , where . The work done on the body during the

Question

A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 {m/s}^{2}, β = 1 m/s, γ = 1 m$ . The work done on the body during the time interval $t = 2$ s to $t = 3$ s is ______ J. [2026]

Smart Achievers · Accepted Answer

(4)

$x (t) = t^{2} + t + 1$

$v (t) = 2 t + 1$

$a (t) = 2$

$F = 4 N$

$t = 3$

$= 13 - 7 = 6 m$

$W = F \cdot S = 4 \times 6 = 24 J$

Solution

Q.
A body of mass 2 kg is moving along x-direction such that its displacement as function of time is given by $x (t) = α t^{2} + β t + γ m$ , where $α = 1 {m/s}^{2}, β = 1 m/s, γ = 1 m$ . The work done on the body during the time interval $t = 2$ s to $t = 3$ s is ______ J. [2026]

1 42

2 49

3 12

4 24

Ans.
(4)

$x (t) = t^{2} + t + 1$

$v (t) = 2 t + 1$

$a (t) = 2$

$F = 4 N$

$Displacement = x (3) - x (2)$

$= 13 - 7 = 6 m$

$W = F \cdot S = 4 \times 6 = 24 J$

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