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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.
$ -8 \,m/s^2$ and $ -30000\, kg\, m\, s^{-1}$ , $2000\, N$
$ -1 \,m/s^2$ and $ -28000\, kg\, m\, s^{-1}$ , $8000\, N$
$ -5 \,m/s^2$ and $ -24000\, kg\, m\, s^{-1}$ , $6000\, N$
$ -2 \,m/s^2$ and $ -42000\, kg\, m\, s^{-1}$ , $5000\, N$
Solution
Mass of the motor car, $m = 1200\, kg$
Initial velocity of the motor car, $u = 90\, km/h = 25 \,m/s$
Final velocity of the motor car, $v = 18\, km/h = 5\, m/s $
Time taken, $t = 4\, s$
According to the first equation of motion:$ v = u + at$
$5 = 25 + a (4)$
$a = -5\, m/s^2$
Negative sign indicates that its a retarding motion i.e. velocity is decreasing.
Change in momentum $= mv -mu = m (v -u)$
$= 1200 (5 -25) = -24000\, kg\, m\, s^{-1}$
Force = Mass $\times $ Acceleration
$= 1200 \times -5 = -6000\, N$
Acceleration of the motor car $= -5 \,m/s^2$
Change in momentum of the motor car $= -24000\, kg\, m\, s^{-1}$
Hence, the force required to decrease the velocity is $6000\, N$.
(Negative sign indicates retardation, decrease in momentum and retarding force)
