Question

A car accelerates uniformly from 18km/hr to 36km/hr in 5 min .the acceleration is
a.5 m/s^2
b.1 km/s^2
c.216 km/s^2
d.216 km/hr^2​

Answer 1

Answer:

• The acceleration is 216 km/hr^2. Henceforth, option d. is correct.

Explanation:

Provided that:

• Initial velocity = 36 kmph
• Final velocity = 18 kmph
• Time = 5 minutes

To determine:

• Acceleration

Solution:

• Acceleration = 216 kmph sq.

Using concepts:

• We can use either first equation of motion or acceleration formula to solve this question.

• Formula to convert min into hr

Using formulas:

✡️ First equation of motion is given by the mentioned formula:

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

✡️ Acceleration formula:

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

✡️ Formula to convert minutes into hours is mentioned below:

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

Required solution:

✴️ Firstly let us convert minutes into hours by using suitable formula!

$:\implies \sf 1 \: min \: = \dfrac{1}{60} \: hr \\ \\ :\implies \sf 5 \: min \: = \dfrac{5}{60} \: hr \\ \\ :\implies \sf 5 \: min \: = \dfrac{1}{12} \: hr \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

✴️ Now let us find out the acceleration by using first equation of motion!

$:\implies \sf v \: = u \: + at \\ \\ :\implies \sf 36 = 18 + a(\dfrac{1}{12}) \\ \\ :\implies \sf 36 - 18 = \dfrac{1}{12}a \\ \\ :\implies \sf 18 = \dfrac{a}{12} \\ \\ :\implies \sf a \: = 18 \times 12 \\ \\ :\implies \sf a \: = 216 \: kmph^2$

• Henceforth, 216 km/hr^2 is the correct answer. Therefore, option d. is correct.

You can find out the acceleration by using acceleration formula too.

_____________________

Now let's find out the acceleration in the international system unit too.

Provided that:

• Initial velocity = 36 kmph
• Final velocity = 18 kmph
• Time = 5 minutes

To determine:

• Acceleration

Solution:

• Acceleration = 1/60 mps sq.

Using concepts:

• We can use either first equation of motion or acceleration formula to solve this question.

• Formula to convert kilometre per hour into metre per second.

• Formula to convert min into sec.

Using formulas:

✡️ First equation of motion is given by the mentioned formula:

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

✡️ Acceleration formula:

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

✡️ Formula to convert kmph-mps:

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

✡️ Formula to convert min to sec:

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

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

Required solution:

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

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

✴️ Now let us convert initial velocity into metre per second!

$:\implies \sf 18 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{18} \times \dfrac{5}{\cancel{{18}}} \: (Cancelling) \\ \\ :\implies \sf 5 ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

✴️ Now let us convert minutes into seconds by using suitable formula!

$:\implies \sf 1 \: min \: = 60 \: sec \\ \\ :\implies \sf 5 \: min \: = 5 \times 60 \: sec \\ \\ :\implies \sf 5 \: min \: = 300 \: seconds \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

✴️ Now let us find acceleration!

By using acceleration formula...

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{dv}{dt} \\ \\ :\implies \sf a \: = \dfrac{\Delta v}{t} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a =\dfrac{10-5}{300} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{5}{300} \\ \\ :\implies \sf a \: = \dfrac{1}{60} \: ms^{-2}$

• You can find out the acceleration by using first equation of motion too.