Question

a car moves 90km/h after 30 minutes its velocity becomes 108km/h . find its accleration​

Answer 1

Provided that:

• Initial velocity = 90 kmph
• Final velocity = 108 kmph
• Time = 30 minutes

To calculate:

• Acceleration

Solution:

• The acceleration = 1/360 m/s²

Using concepts:

• Acceleration formula
• Formula to convert kmph-mps
• Formula to convert min-sec

Using formulas:

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

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

• ${\small{\underline{\boxed{\pmb{\sf{1 \: min \: = 60 \: seconds}}}}}}$

Required solution:

~ Firstly let us convert kmph-mps!

Converting 90 kmph-mps first!

$:\implies \sf 90 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{90} \times \cancel{\dfrac{5}{18}} \\ \\ :\implies \sf 5 \times 5 \\ \\ :\implies \sf 25 \: mps \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

Now converting 108 kmph-mps!

$:\implies \sf 108 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{108} \times \cancel{\dfrac{5}{18}} \\ \\ :\implies \sf 6 \times 5 \\ \\ :\implies \sf 30 \: mps \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

Therefore,

• Initial velocity, u = 25 mps
• Final velocity, v = 30 mps

~ Now let's convert min into seconds!

$:\implies \sf 1 \: min \: = 60 \: seconds \\ \\ :\implies \sf 30 \: min \: = 30 \times 60 \: seconds \\ \\ :\implies \sf 30 \: min \: = 1800 \: seconds \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

~ Now let us find out the acceleration!

$:\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{30-25}{1800} \\ \\ :\implies \sf a \: = \dfrac{5}{1800} \\ \\ :\implies \sf a \: = \dfrac{1}{360} \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = \dfrac{1}{360} \: ms^{-2}$