Question

A bus decreases its speed from $80km{h^{ - 1}}$ to $60km{h^{ - 1}}$ in 5s. Find the acceleration of the bus.

Answer 1

Hint: In order to solve this question first of all we need to find the difference between the given speeds. After that we need to divide the difference by the given time. Then only we can conclude with the correct solution of the given question.

Complete step by step solution:
Initial speed of the bus is given as,${v_i} = 80km{h^{ - 1}}$
Let us convert the velocity in$m{s^{ - 1}}$.
Therefore, ${v_1} = 80 \times \dfrac{5}{{18}} = 22.22m{s^{ - 1}}$
The final speed of the bus is given as,${v_f} = 60km{h^{ - 1}}$
Let us also convert it in$m{s^{ - 1}}$.
Therefore, ${v_f} = 60 \times \dfrac{5}{{18}} = 16.66m{s^{ - 1}}$
The time taken to change the speed is given as,$t = 5s$
Already we know that acceleration is given by,
$a = \dfrac{{{v_f} - {v_i}}}{t}$
$\Rightarrow a = \dfrac{{16.66 - 22.22}}{5}$
$\therefore a = - 1.112m{s^{ - 2}}$
Therefore, the required value of acceleration is $ - 1.112m{s^{ - 2}}$.
Hence, the bus is retarding with an acceleration of $ - 1.112m{s^{ - 2}}$.
Here, the $ - ve$ sign of acceleration denotes that there is retardation in speed or deceleration is taking place.

Note: We define acceleration as the change of rate of velocity of an object with respect to time. Deceleration is not the opposite of acceleration. We say that there is deceleration in an object when the acceleration is causing a decrease in speed. It will be incorrect to represent deceleration as a negative time rate of change of velocity. Acceleration denotes the increase in speed whereas deceleration refers to the reduction in speed of a body. Acceleration is a vector quantity. Deceleration is the opposite of acceleration. Deceleration is also known as retardation. We can also define deceleration as a decrease in speed as the body moves away from the starting point.