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Question

A force F = (3x + 4) newton displaces an object of mass 10 kg from x = 0 to x = 4m. If the speed of the object at x = 0 is 2ms^-1, its speed at x = 4m will be ___m/s

Moderate

Solution

Work done by the force is
$\begin{array}{l} dW = fdx \\ W = \int_{0}^{4} (3 x + 4) dx \\ = {|\frac{3 x^{2}}{2} + 4 x|}_{0}^{4} = 40 J \end{array}$
From work energy principle, work done = change in kinetic energy.
$\begin{array}{l} W = Δk = \frac{1}{2} m (v^{2} - u^{2}) \\ 40 = \frac{1}{2} \times 10 \times (v^{2} - 2^{2}) \\ \Rightarrow v = 2 \sqrt{3} = 3.46 {ms}^{- 1} \end{array}$

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Work

Unlock the full solution & master the concept.

A force F = (3x + 4) newton displaces an object of mass 10 kg from x = 0 to x = 4m. If the speed of the object at x = 0 is 2ms-1, its speed at x = 4m will be ___m/s

Work done by the force isdW=fdxW=∫04 (3x+4)dx =3x22+4x04=40JFrom work energy principle, work done = change in kinetic energy. W=Δk=12mv2−u2 40=12×10×v2−22⇒v=23=3.46ms−1

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A force F = (3x + 4) newton displaces an object of mass 10 kg from x = 0 to x = 4m. If the speed of the object at x = 0 is 2ms^-1, its speed at x = 4m will be ___m/s