First slide

Work

Question

A force of $F=(3+5 x) \hat{i} N$ displaces a particle from (1,0,0)m to (3,5,-2) m. The work done is

Moderate

A

54J
B

28J
C

-54J
D

26J

Solution

$\begin{array}{l} W = \int \vec{F} \cdot \vec{d x} = \int (3 + 5 x) d x \\ W = 3 \int_{1}^{3} d x + 5 \int_{1}^{3} x d x \\ W = 3 [x]_{1}^{3} + 5 {[\frac{x^{2}}{2}]}_{1}^{3} = (3 \times 2) + (\frac{5}{2} \times 8) \\ W = 6 + 20 = 26 J \end{array}$

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