Question

A bus decreases its speed from 80 km h−1 to 60 km h−1 in 5 s. Find the acceleration of the bus.

Answer 1

Given :-

Initial velocity of bus = 80km/h

final velocity = 60 km/h

time = 5 seconds

• We have to find the acceleration of bus

Using 1st equation of motion

$\boxed{\sf v= u+at}$

First convert their velocity into m/s

$\sf 1km/h = \dfrac{5}{18}m/s\\ \\ \longrightarrow\sf u= 80\times \dfrac{5}{18}= \cancel{\dfrac{400}{18}}\\ \\ \longrightarrow\sf u= \dfrac{200}{9} m/s\\ \\ \longrightarrow\sf v = 60\times \dfrac{5}{18} =\cancel{\dfrac{300}{18}}\\ \\ \longrightarrow\sf v= \dfrac{150}{9}m/s$

• Now find the acceleration

$\longrightarrow\sf v= u+at\\ \\ \longrightarrow\sf \dfrac{150}{9}= \dfrac{200}{9}+ a\times 5\\ \\ \longrightarrow\sf \dfrac{150}{9}-\dfrac{200}{9} = 5a\\ \\ \longrightarrow\sf \dfrac{150-200}{9}= 5a\\ \\ \longrightarrow\sf \dfrac{\cancel{-50}}{9}\times \dfrac{1}{\cancel{5}}=a\\ \\ \longrightarrow\sf \dfrac{-10}{9}=a\\ \\ \longrightarrow\sf \ or \ a= -1.11m/s^2$

$\underline{\boxed{\sf\ \ Acceleration= (-1.11m/s^2)}}$

Answer 2

Acceleration of bus is -1.11 m/s²

Explanation :

Initial speed of bus = 80 km/h

= 80 × (5/18) m/s

= 22.22 m/s

Final speed of bus = 60 km/h

= 60 × (5/18) m/s

= 16.67 m/s

Time taken = 5 s

We will use 1st equation of motion for finding acceleration.

⇒ v = u + at

⇒ 16.67 = 22.22 + a × 5

⇒ 16.67 - 22.22 = 5a

⇒ -5.55 = 5a

⇒ a = -5.55/5

⇒ a = -1.11 m/s²

∴ Acceleration of bus = -1.11 m/s²