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An object of mass $100 \,kg $ is accelerated uniformly from a velocity of $5\, m \,s^{-1}$ to $ 8 \,m \,s^{-1}$ in $6\, s$. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.
$100 \,kg \,ms^{-1}$ and $200 \,kg\, ms^{-1}$ , $30\, N$
$300 \,kg \,ms^{-1}$ and $500 \,kg\, ms^{-1}$ , $20\, N$
$400 \,kg \,ms^{-1}$ and $600 \,kg\, ms^{-1}$ , $40\, N$
$500 \,kg \,ms^{-1}$ and $800 \,kg\, ms^{-1}$ , $50\, N$
Solution
Initial velocity of the object, $ u = 5\, m/s$
Final velocity of the object, $ v = 8\, m/s$
Mass of the object, $m = 100\, kg$
Time take by the object to accelerate, $t = 6\, s$
Initial momentum $= mu = 100 \times 5 = 500 \,kg\, ms^{-1}$
Final momentum $= mv= 100 \times 8 = 800 \,kg\, ms^{-1}$
Force exerted on the object,
$F=\frac{m v-m u}{t}$
$=\frac{m(v-u)}{t}=\frac{800-500}{6}=\frac{300}{6}=50 \,N$
Initial momentum of the object is $500 \,kg \,ms^{-1}$.
Final momentum of the object is $800 \,kg\, ms^{-1}$.
Force exerted on the object is $50\, N$.
