Question

The bus decreases its speed from 60Km/hr to 30Km/hr in 5 seconds . Find the acceleration of the bus.

Answer 1

Hint: We know the basics of a particle in a single dimension. We have to find the acceleration of the bus. Acceleration is defined as change in rate of velocity. By applying simple equations of motion we can obtain the result.

Formula used:
$v=u+at$

Complete step by step answer:
Here, we have v = 30km/hr u = 30km/hr and t = 5s
We know the first basic equation of motion
$v=u+at$
$\begin{align}
  & 30=60+a\times 5 \\
 & \Rightarrow 30-60=a\times 5 \\
 & \Rightarrow -30=5a \\
 & \Rightarrow a=\dfrac{-30}{5} \\
 & \Rightarrow a=-6 \\
\end{align}$
Therefore, we obtain acceleration = $- 6 m/{{s}^{2}}$.
Here, the minus sign indicates that the bus is undergoing retardation.

Additional Information:
Equations of motion are the mathematical formulas that describe the position, velocity, or acceleration of a body relative to a given frame of reference. Hence, these equations are needed to derive the components like displacement(s), velocity (initial and final), time(t) and acceleration(a). Therefore they will only be applied when acceleration is constant and motion may be a line . Equations of motion relate the displacement of an object with its velocity, acceleration and time. The motion of an object can follow many different paths. Here we will focus on motion in a straight line (one dimension). We can therefore just use positive and negative magnitudes of the displacement, velocity and acceleration, where negative values are in the opposite direction to positive quantities.
First equation of motion
\[v=u+at\]

Second equation of motion
\[s=ut+\dfrac{1}{2}a{{t}^{2}}\]

Third equation of motion:
\[{{v}^{2}}={{u}^{2}}+2as\]

Note:
Let us have a glimpse on acceleration and retardation to avoid mistakes.
Acceleration of a body is defined because the rate of change of its velocity with time. Retardation means negative acceleration. If the speed of a body decreases,the acceleration is negative. Example: The acceleration of a body is $-6\text{m}{{\text{s}}^{\text{-2}}}$ .