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

Provided that:

• Initial velocity = 80 kmph
• Final velocity = 60 kmph
• Time taken = 5 seconds

To calculate:

• The acceleration

Solution:

• The acceleration = -1.112 mps sq.

Using concepts:

• Acceleration formula
• Formula to convert kmph-mps

Using formulas:

• Acceleration is given by:

• ${\small{\underline{\boxed{\pmb{\sf{a \: = \dfrac{v-u}{t}}}}}}}$

• Formula to convert kmph-mps:

• ${\small{\underline{\boxed{\pmb{\sf{1 \: kmph \: = \dfrac{5}{18} \: mps}}}}}}$

Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity and t denotes time taken.

Required solution:

~ Firstly let us convert kmph-mps!

Converting 80 kmph-mps

$:\implies \sf 1 \: kmph \: = \dfrac{5}{18} \: mps \\ \\ :\implies \sf 80 \: kmph \: = 80 \times \dfrac{5}{18} \: mps \\ \\ :\implies \sf 80 \: kmph \: = \dfrac{400}{18} \: mps \\ \\ :\implies \sf 80 \: kmph \: = 22.22 \: mps \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

Converting 60 kmph-mps

$:\implies \sf 1 \: kmph \: = \dfrac{5}{18} \: mps \\ \\ :\implies \sf 60 \: kmph \: = 60 \times \dfrac{5}{18} \: mps \\ \\ :\implies \sf 60 \: kmph \: = \dfrac{300}{18} \: mps \\ \\ :\implies \sf 60 \: kmph \: = 16.66 \: mps \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

~ Now let us convert acceleration by using suitable formula!

$:\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{16.66-22.22}{5} \\ \\ :\implies \sf a \: = \dfrac{-5.56}{5} \\ \\ :\implies \sf a \: = -1.112 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = -1.112 \: ms^{-2} \\ \\ :\implies \sf Retardation \: = -1.112 \: ms^{-2}$