Question

After application of brakes, a car slows down from 108 kmh-1 to 36 kmh-1 in 8s. Calculate retardation in SI unit.

Answer 1

Answer:

2.5 m/s²

Explanation:

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

• Initial velocity (u) = 108 km/h
• Final velocity (v) = 36 km/h
• Time taken (t) = 8 s

We are asked to to calculate retardation in SI unit. SI unit of retardation is m/s². It is as same as acceleration but the difference is that it is negative acceleration.

So, in order to calculate retardation in m/s, we need to convert velocities in m/s.

Converting initial velocity in m/s :

$\longmapsto \rm{ u = 180 \; kmh^{-1} }$

• 1 km/h = 5/18 m/s

$\longmapsto \rm{ u = \Bigg ( 108 \times \dfrac{5}{18} \Bigg ) \; ms^{-1} }$

$\longmapsto \rm{ u = \Big (6 \times 5 \Big ) \; ms^{-1} }$

$\longmapsto \bf { u = 30 \; ms^{-1} }$

Converting final velocity in m/s :

$\longmapsto \rm{ v = 36 \; kmh^{-1} }$

• 1 km/h = 5/18 m/s

$\longmapsto \rm{ v = \Bigg ( 36 \times \dfrac{5}{18} \Bigg ) \; ms^{-1} }$

$\longmapsto \rm{ v = \Big (2 \times 5 \Big ) \; ms^{-1} }$

$\longmapsto \bf { v = 10 \; ms^{-1} }$

$\rule{200}2$

Now, in order to calculate retardation, we need to find the acceleration first. 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

$\longmapsto \rm {10 = 30 + 8a }$

$\longmapsto \rm {10 -30 = 8a }$

$\longmapsto \rm {-20= 8a }$

$\longmapsto \rm {\dfrac{-20}{8}= a }$

$\longmapsto \rm {-2.5 \; ms^{-2} = a }$

Now, as the acceleration has negative sign. So, the retardation will have positive sign

$\longmapsto \rm {2.5 \; ms^{-2} = Retardation}$

∴ Retardation is 2.5 m/s².