A body of mass 5 kg resting on a smooth horizontal plane, is acted upon by force 6i + 2j, 5i + 4j and 4i - j. Calculate the:
(a) velocity of the body
(b) Magnitude of its velocity after 4s.
(a) Resultant of the forces acting on the plane = (6i + 2j) + (5i + 4j) + (4i - j) = 15i + 5j
\(F = \frac{m \Delta v}{t}\)
Resultant force = \(\frac{mv}{t} \)
\(15i + 5j = \frac{5v}{t}\)
\(v = \frac{(15i + 5j). t}{5} = 3t i + t j\)
(b) velocity after 4 seconds = \(3(4) i + 4 j = 12 i + 4 j\)
\(\therefore |12i + 4j| = \sqrt{12^{2} + 4^{2}} = \sqrt{144 + 16}\)
= \(\sqrt{160} \)
= \(4\sqrt{10} m/s\)
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