Question

If the speed of a car increases from 36 km/h to 72 km/h in 10 seconds, find the acceleration of the car.​

Answer 1

Answer:

Provided that:

• Time = 10 seconds
• Initial velocity = 36 kmph
• Final velocity = 72 kmph

To calculate:

• The acceleration

Solution:

• The acceleration = 1 mps sq.

Using concepts:

• We can use acceleration formula or first equation of motion too for finding acceleration.

• Formula to convert kmph-mps.

Using formulas:

• Acceleration is given by,

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

• First equation of motion:

• ${\small{\underline{\boxed{\sf{v \: = u \: + at}}}}}$

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

Required solution:

~ Firstly let us convert initial velocity into metre per second!

$\begin{gathered}:\implies \sf 36 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{36} \times \dfrac{5}{\cancel{{18}}} \\ \\ :\implies \sf 2 \times 5 \\ \\ :\implies \sf 10 \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}\end{gathered}$

~ Now let us convert final velocity into metre per second!

$\begin{gathered}:\implies \sf 72 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{72} \times \dfrac{5}{\cancel{{18}}} \\ \\ :\implies \sf 4 \times 5 \\ \\ :\implies \sf 20 \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}\end{gathered}$

Therefore,

• Initial velocity = 10 mps
• Final velocity = 20 mps

~ Now let's find out the acceleration!

By using acceleration formula!

$:\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{20-10}{10} \\ \\ :\implies \sf a \: = \dfrac{10}{10} \\ \\ :\implies \sf a \: = 1 \: mps^{-2} \\ \\ :\implies \sf Acceleration \: = 1 \: mps^{-2}$

By using first equation of motion!

$:\implies \sf v \: = u \: + at \\ \\ :\implies \sf 20 = 10 + a(10) \\ \\ :\implies \sf 20 - 10 = 10a \\ \\ :\implies \sf 10 = 10a \\ \\ :\implies \sf a \: = \dfrac{10}{10} \\ \\ :\implies \sf a \: = 1 \: mps^{-2} \\ \\ :\implies \sf Acceleration \: = 1 \: mps^{-2}$