Question

A bus decreases its speed from 80 kmph to 60 kmph in 5s. Find the acceleration of the bus.

Answer 1

Hint: One of the equations of motion formula should be used to solve this problem. The law of motion formula that relates the initial velocity, the final velocity, the acceleration and the time will be used to solve this problem. As this is a direct question, using the given values, we can solve this problem.

Formula used:
\[v=u+at\]

Complete step by step solution:
The law of motion formula that relates the initial velocity, the final velocity, the acceleration and the time is given as follows.
\[v=u+at\]
Where v represents the final velocity, u represents the initial velocity, a represents the acceleration and t represents the time.
From the data, we have the data as follows.
The initial velocity of the bus, \[u=80\,\text{kmph}\]
The final velocity of the bus, \[v=50\,\text{kmph}\]
The time taken by the bus, \[t=5\,s\]
Firstly, we will convert the units given parameters to the SI unit.
The initial velocity of the bus, \[u=80\,\text{kmph}\]
\[\begin{align}
  & u=80\,\times \dfrac{5}{18} \\
 & u=22.22\,{}^{m}/{}_{s} \\
\end{align}\]
Therefore, the initial velocity of the bus, \[u=22.22\,{}^{m}/{}_{s}\]
The final velocity of the bus, \[v=50\,\text{kmph}\]
\[\begin{align}
  & v=50\,\times \dfrac{5}{18} \\
 & v=16.67\,{}^{m}/{}_{s} \\
\end{align}\]
Therefore, the initial velocity of the bus, \[v=16.67\,{}^{m}/{}_{s}\]
Now, we will compute the acceleration of the bus. So, we get,
The law of motion formula is,
\[v=u+at\]
Substitute the given values of the initial velocity, final velocity and the time taken by the bus.
\[\begin{align}
  & 16.67=22.22+a(5) \\
 & 16.67-22.22=5a \\
\end{align}\]
Continue the further calculation. So, we get,
\[\begin{align}
  & -5.55=5a \\
 & a=-1.11{m}/{{{s}^{2}}}\; \\
\end{align}\]
The negative sign represents the retardation.
\[\therefore \] The value of the acceleration of the bus obtained is \[-1.11{m}/{{{s}^{2}}}\;\].

Note:
The formulae of laws of motion should be known to solve this type of problem. The units of the parameters should be taken care of. In this problem, we have converted the units of the parameters to SI units.