Question

# A motorcar of mass $1200kg$ is moving along a straight line with a uniform velocity of $90km/h$. Its velocity is slowed down to $18km/h$ in $4s$ by an unbalanced external force. calculate the acceleration and change in momentum. also, calculate the magnitude of the force required.

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Solution

## Step 1: Given data.The mass of the motorcar is $1200kg$.The initial velocity of the car is $90km/h$.The final velocity of the care is $18km/h$.The time of acceleration is $4s$.Step 2: Concept and formula to be used.The formula of momentum $p$ is mass $m$ multiplies by velocity $v$, that is $p=mv$.The change in momentum $△p$ is given by final momentum ${p}_{2}$ minus initial momentum ${p}_{1}$, that is $△p={p}_{2}-{p}_{1}$.According to the equation of motion, $v=u+at$.The magnitude of the force is given by $F=m\left|a\right|$.Step 3: Find the acceleration of the motorcar.Since the motorcar slowed down from $90km/h$ to $18km/h$ in $4s$.So, the initial speed is $90km/h$, the final speed is $18km/h$ and the time is $4s$.Convert the speed in $m/s$.So, $90km/h$ is equal to $25m/s$ and $18km/h$ is equal to $5m/s$So, the acceleration $a$ of the motorcar is given by:$5=25+4a\phantom{\rule{0ex}{0ex}}⇒4a=-20\phantom{\rule{0ex}{0ex}}⇒a=-5$Therefore, the acceleration of the motorcar is $-5m/{s}^{2}$.Step 4: Find the change in momentum of the motorcar.Since, the mass of the motorcar is $1200kg$ and the initial velocity is $25m/s$.So, the initial momentum ${p}_{1}$ is given by:${p}_{1}=1200·25\phantom{\rule{0ex}{0ex}}⇒{p}_{1}=30000$Since, the final velocity is $5m/s$.So, the final momentum ${p}_{2}$ is given by:${p}_{2}=1200·5\phantom{\rule{0ex}{0ex}}⇒{p}_{2}=6000$So, the change in momentum $△p$ is given by:$△p=6000-30000\phantom{\rule{0ex}{0ex}}⇒△p=-24000$Therefore, the change in momentum is $-24000kg·m/s$.Step 5: Find the magnitude of the required force.Since, the mass of the motorcar is $1200kg$ and the acceleration is $-5m/{s}^{2}$.So, the magnitude of the force $F$ is given by:$F=1200·\left|-5\right|\phantom{\rule{0ex}{0ex}}⇒F=6000$Therefore, the magnitude of the required force is $6000N$.Hence, the acceleration, change in momentum and the magnitude of the force required are $-5m/{s}^{2}$, $-24000kg·m/s$ and $6000N$ respectively.

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