(a) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i – 4 j ) ms^{ -1}\) after 4 seconds . Find the:
acceleration of the particle;
(b) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i – 4 j ) ms^{ -1}\) after 4 seconds . Find the:
magnitude of the force F ;
(c) A particle of mass 2 kg moves under the action of a constant force, F N , with an initial velocity \((3 i + 2 j ) ms^{ -1}\) and a velocity of \((15 i – 4 j ) ms^{ -1}\) after 4 seconds . Find the:
magnitude of the velocity of the particle after 8 seconds , correct to three decimal places.
Explanation
(a) \(m=2kg;u=(3i+2j)ms^{-1};v=(15i-4j)ms^{-1};t=4s;a=?\)
\(a=\frac{v - u}{t}=\frac{(15i - 4j) - (3i + 2j)}{4}\)
\(a=\frac{15i - 4j - 3i - 2j}{4}=\frac{12i - 6j}{4}\)
\(∴a=3i-\frac{3}{2}j ms^{-2}\)
(b) \(m=2kg;a=3i-\frac{3}{2} j\)
\(F=ma=2(3i-\frac{3}{2}j)\)
F = 6i - 3j
\(|F| = √(6^2 + (-3)^2)\)
\(|F| = √(36 + 9) = √45\)
\(∴ |F| = 3√5 N = 6.71 N\)
(c) \(u=3i+2jms^{-1};a=3i-\frac{3}{2}j ms^{-2};t=8s\)
v = u + at
\(v=(3i+2j)+8(3i-\frac{3}{2} j)\)
\(v = 3i + 2j + 24i - 12j\)
\(v = 27i - 10j\)
\(|v| = √(27^2 + (-10)^2)\)
\(|v| = √(729 + 100) = √829\)
\(∴ |v| = 28.792 ms^{-1} (to 3d.p)\)