First slide

Work

Question

The velocity of a moving particle varies with distance moved as $v = (4 + 3 x) m s^{- 1}$ . If mass of the particle is 1kg, then the work done on the particle during the time its displacement changes from $x = 1 m$ to $x = 2 m$ is______

Moderate

Solution

$\begin{array}{l} v = 4 + 3 x a = v \frac{d v}{d x} = (4 + 3 x) \times 3 \\ a = 3 [4 + 3 x] \\ W = \int ma d x = \int_{1}^{2} 1 \times 3 (4 + 3 x) d x \\ W = 3 [4 [x]_{1}^{2} + 3 {[\frac{x^{2}}{2}]}_{1}^{2}] = 2 [4 \times (2 - 1) + \frac{3}{2} (4 - 1)] \\ W = 3 [4 + \frac{3}{2} \times 3] = 3 [4 + 4.5] = 3 \times 8.5 \\ W = 25.5 J \end{array}$

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