First slide

Second law

Question

A 15 kg block is initially moving along a smooth horizontal surface with a speed of v = 4 m/s to the left. It is acted by a force F, which varies in the manner shown. Determine the velocity of the block at t = 15 seconds.
Given that, $F = 40 \cos (\frac{π}{10}) t$ .

Moderate

A

12.5 m/s
B

8.5 m/s
C

20 m/s
D

9.5 m/s

Solution

Change in linear momentum $∆ P = \int F dt$
$15 (v_{f} + u) = \int_{0}^{15} 40 \cos (\frac{π}{10}) t dt$
$v_{f} = - 4 + \frac{40}{15} {[\frac{\sin (\frac{π}{10}) t}{\frac{π}{10}}]}^{15}_{0} m / s$
=-4 + $\frac{400}{15 π} (- 1) = - 12.5 m / s$

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