Question

A scooterist applies brakes and brings his scooter to rest in 1.5 s. If the retardation of the brakes is 5 m/s2,calculate the initial velocity of the scooter in (i) SI system (ii) km /h.

Answer 1

Answer:

In m/s = 7.5 m/s

In km/h = 27 km/h

Explanation:

As per the provided information in the given question, we have :

• Final velocity (v) = 0 m/s (Because it applies brakes and stops)
• Time taken (t) = 1.5 s
• Acceleration (a) = –5 m/s² (Since, retardation is +5 m/s²)

We are asked to calculate,

• Initial velocity (u) of car in SI system and in km/h.

Calculating initial velocity in m/s :

SI system refers to the SI unit of initial velocity, here. SI unit of initial velocity is m/s.

By using the first equation of motion,

$\longmapsto \bf { v = u + at}$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time

$\longmapsto \rm { 0 = u + (-1.5 \times 5)}$

$\longmapsto \rm { 0 = u + (-7.5)}$

$\longmapsto \rm { 0 = u-7.5}$

$\longmapsto \rm { 0 +7.5 = u}$

$\longmapsto \bf { 7.5 \; ms^{-1} = u}$

∴ Initial velocity in m/s is 7.5 m/s.

Calculating initial velocity in km/h :

It is easy to find the initial velocity in km/h if we have initial velocity in m/s. We just need to convert m/s into km/h.

• 1 m/s = 18/5 km/h

$\longmapsto \rm { u = 7.5 \; ms^{-1}}$

$\longmapsto \rm { u =\Bigg ( 7.5 \times \dfrac{18}{5} \Bigg ) \; kmh^{-1}}$

$\longmapsto \rm { u =\Bigg ( \dfrac{75}{10} \times \dfrac{18}{5} \Bigg ) \; kmh^{-1}}$

$\longmapsto \rm { u =\Bigg ( \dfrac{15}{10} \times 18 \Bigg ) \; kmh^{-1}}$

$\longmapsto \rm { u =\Bigg ( \dfrac{270}{10} \Bigg ) \; kmh^{-1}}$

$\longmapsto \bf { u = 27 \; kmh^{-1}}$

∴ Initial velocity in km/h is 27 km/h.