Question

A bus decrease its speed from 18km/h to 36 km /h in 5seconds. Find the accelaration of the bus

Answer 1

Answer:

Acceleration = 1 m/s²

Explanation:

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

• Initial velocity (u) = 18 km/h
• Final velocity (v) = 36 km/h
• Time taken (t) = 5 s

We are asked to calculate the acceleration.

Let us first convert the velocities in their standard form, that is m/s.

Converting final velocity in m/s :

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

• 1 km/h = 5/18 m/s

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

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

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

Converting initial velocity in m/s :

$\longmapsto \rm { u = 18 \; kmh^{-1} }$

• 1 km/h = 5/18 m/s

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

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

$\longmapsto \bf { u =5 \; ms^{-1} }$

$\rule{200}2$

Calculating acceleration :

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

$\longmapsto \rm { 10 = 5 + 5a}$

$\longmapsto \rm { 10 -5 = 5a}$

$\longmapsto \rm { 5 = 5a}$

$\longmapsto \rm { \cancel{\dfrac{5}{5}} = a}$

$\longmapsto \bf { 1 \; ms^{-2} = a}$

∴ Acceleration is 1 m/s².

$\rule{200}2$

About acceleration :

• Acceleration is defined as the rate of change in velocity.

• It SI unit is m/s².

• It is a vector quantity, that means it requires both magnitude and direction for its description.

• Negative acceleration is called retardation.

Formula to calculate acceleration:

$\longmapsto \bf { a = \dfrac{v-u}{t} }$

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