First slide

Newton's laws of motion

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 $Δ P = \int F d t$
$\begin{array}{l} 15 (v_{f} + u) = \int_{0}^{15} 40 \cos (\frac{π}{10}) t d t \\ v_{f} = - 4 + \frac{40}{15} {[\frac{\sin (π / 10) t}{π / 10}]}_{0}^{15} = - 4 + \frac{400}{15 π} (- 1) = - 12.5 m / s \end{array}$

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