First slide

Power

Question

A particle A of mass $\frac{10}{7}$ kg is moving in the positive direction of X. Its initial position is x=0 and initial velocity is 1m/sec. The velocity at x = 10m is …..

Moderate

A

4 m/sec
B

2 m/sec
C

$3 \sqrt{2}$ m/sec
D

$\frac{100}{3}$ m/sec

Solution

Area of the graph = $∫pdx=area$ of the trapezium = $\frac{1}{2} (4 + 2) \times 10 = 30$
$∫pdx=30$
$∫Fvdx=30$
$∫ \frac{m d v}{d t} v d x = 30$
$∫mdv.v \frac{dx}{dt} = 30$
${∫mv}^{2} dv = 30$
$m {|\frac{v^{3}}{3}|}_{1}^{u} = 30$
$u=4m/s$

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