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.

Answer 1

Step 1: Given data.

1. The mass of the motorcar is $1200kg$.
2. The initial velocity of the car is $90km/h$.
3. The final velocity of the care is $18km/h$.
4. The time of acceleration is $4s$.

Step 2: Concept and formula to be used.

1. The formula of momentum $p$ is mass $m$ multiplies by velocity $v$, that is $p=mv$.
2. The change in momentum $△p$ is given by final momentum $p_2$ minus initial momentum $p_1$, that is $△p=p_2-p_1$.
3. According to the equation of motion, $v=u+at$.
4. 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:

$$\begin{gathered} 5=25+4a \\ \Rightarrow 4a=-20 \\ \Rightarrow a=-5 \end{gathered}$$

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:

$$\begin{gathered} p_1=1200·25 \\ \Rightarrow p_1=30000 \end{gathered}$$

Since, the final velocity is $5m/s$.

So, the final momentum $p_2$ is given by:

$$\begin{gathered} p_2=1200·5 \\ \Rightarrow p_2=6000 \end{gathered}$$

So, the change in momentum $△p$ is given by:

$$\begin{gathered} △p=6000-30000 \\ \Rightarrow △p=-24000 \end{gathered}$$

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:

$$\begin{gathered} F=1200·\left|-5\right| \\ \Rightarrow F=6000 \end{gathered}$$

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.