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06/01/2021 4:36 pm
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A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.
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06/01/2021 4:42 pm
Here, mass m = 1200 kg
Initial velocity, u = 90 km h-1
= 90 x 5/18 = 25 m s-1
Final velocity, v = 18 km h-1
= 18 x 5/18 = 5 m s-1
Time, t = 4 s
(i) Acceleration, a = \(\frac{Change\;in\;velocity}{Time}\)
= \(\frac{v-u}{t}\) = \(\frac{5 - 25}{4}\)= \(-5 \;m s^{-2}\)
(ii) Change in momentum
= mv - mu = m(v - u)
= 1200(5 -25)
= -24000 kg ms-1
Magnitude of change in momentum
= 24000 kg ms-1
(iii) Force, F = ma = 1200(-5) = -6000 N
∴Magnitude of force = 6000 N