Question

Example 8.6 A car accelerates uniformly
from 18 km h to 36 km h in 5 s.
Calculate (I) the acceleration and (ii) the
distance covered by the car in that time.​

Answer 1

$\huge\underline{\underline{\bf \green{Question-}}}$

A car accelerates uniformly from 18 km h to 36 km h in 5 s.

Calculate

(i) the acceleration and

(ii) the distance covered by the car in that time

$\huge\underline{\underline{\bf \green{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• Initial velocity ( u ) = 18 km/h

❏ Initial velocity in m/s

$\implies{\sf 18×\dfrac{5}{18}}$

$\implies{\sf 5\:m/s}$

• Final Velocity ( v ) = 36 km/h

❏ Final Velocity in m/s

$\implies{\sf 36×\dfrac{5}{18}}$

$\implies{\sf 10\:m/s }$

• Time ( t ) = 5 s

$\large\underline{\underline{\sf To\:Find:}}$

• Acceleration ( a )
• Distance ( s )

❍ Acceleration (a) ➝

✪$\large{\boxed{\bf \blue{ a=\dfrac{v-u}{t}}}}$

$\implies{\sf \dfrac{10-5}{5} }$

$\implies{\bf \red{Acceleration (a)=1\:m/s^2} }$

❍ Distance (s) ➝

✪$\large{\boxed{\bf \blue{s = ut+\dfrac{1}{2}at^2} }}$

$\implies{\sf s=5×5+\dfrac{1}{2}×1×(5)^2}$

$\implies{\sf 25+\dfrac{1}{2}×25}$

$\implies{\bf \red{Distance (s)= 37.5\:m}}$

$\huge\underline{\underline{\bf \green{Answer-}}}$

Acceleration ${\bf \red{1\:m/s^2}}$

Distance ${\bf \red{37.5\:m}}$