Work Energy Theorem: Practice Problem & Solution
A body of mass $3\text{ kg}$ is under a constant force which causes a displacement $s$ in meters in it, given by the relation $s = \frac{1}{3} t^2$, where $t$ is in $s$. Work done by the force in $2\text{ s}$ is: (2006)
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Work Energy Theorem. Understanding the underlying formula is key to arriving at the correct answer below:
Find acceleration by differentiating displacement twice: $v = \frac{2}{3}t$ and $a = \frac{2}{3}\text{ m/s}^2$. Force is $F = ma = 2\text{ N}$. At $t = 2\text{ s}$, displacement is $s = \frac{4}{3}\text{ m}$. Work done $W = F \times s = \frac{8}{3}\text{ J}$.
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