Question

A bus moving with a velocity of $60km\,h{{r}^{-1}}$ has a weight of $50\,tons$. Find out the force required to stop it in $10s$.

Answer 1

Hint: A bus is moving with a certain velocity and needs to be stopped. According to Newton’s second law of motion, force depends on the mass and acceleration of the body. The change in velocity per unit time of a body is acceleration. Convert the units as required, it is recommended to convert units in SI.
Formulas used:
$a=\dfrac{{{v}_{f}}-{{v}_{i}}}{t}$
$F=ma$

Complete answer:
Given, the velocity of the bus is $60km\,h{{r}^{-1}}$, when we convert the velocity in SI units we get,
$\begin{align}
  & 60km\,h{{r}^{-1}}=\dfrac{60\times 1000}{1\times 3600}m{{s}^{-1}} \\
 & \Rightarrow 60km\,h{{r}^{-1}}=\dfrac{50}{3}m{{s}^{-1}} \\
\end{align}$
Therefore, the velocity of the bus in SI units is $\dfrac{50}{3}m{{s}^{-1}}$.
The mass of the bus is $50\,tons$. We know that,
$1ton=907kgs$
Using the above relation we converts tons into kgs as,
$\begin{align}
  & 50tons=50\times 907kgs \\
 & \Rightarrow 50tons=45350kg \\
\end{align}$
Therefore, the mass of the bus in SI units is $45350kg$.
The bus is to be stopped in $10s$, this means that the velocity changes from $\dfrac{50}{3}m{{s}^{-1}}$ to zero in $10s$. We know that,
$a=\dfrac{{{v}_{f}}-{{v}_{i}}}{t}$
Here, $a$ is the acceleration of the bus
${{v}_{f}}$ is the final velocity
${{v}_{i}}$ is the initial velocity
$t$ is the time taken
Given values are substituted in the above equation to calculate acceleration as-
$\begin{align}
  & a=\dfrac{0-\dfrac{50}{3}}{10} \\
 & \Rightarrow a=-\dfrac{5}{3}m{{s}^{-2}} \\
\end{align}$
Therefore, an acceleration of $-\dfrac{5}{3}m{{s}^{-2}}$ is required to bring the bus to rest. The product of mass and acceleration of a body is defined as the force acting on that body. Therefore,
$F=ma$
Here, $F$ is the force
$m$ is the mass
Substituting given values in the above equation, we calculate the force as-
$\begin{align}
  & F=4530kg\times -\dfrac{5}{3}m{{s}^{-2}} \\
 & \Rightarrow F=-7550N \\
\end{align}$
Therefore, the force required to stop the bus is $-7550N$.

Note:
The negative sign indicates that the force is to be applied in the opposite direction to the motion of the bus. According to Newton's second law, the value of force is determined by mass and acceleration of a body, if no acceleration acts on it, the force is zero. In case of zero force, the body is at rest or moves in uniform motion.