Question

A scooter is travelling at 36 km/h. If its velocity increases to 90 km/h in 5 second, then acceleration of scooter in SI UNIT

Answer 1

Anѕwєr :

$\huge\boxed{\red{\sf{3 \; m \: s^{-2} }}}$

Explαnαtion:

As per the provided information in the given question, we have :

• Initial velocity (u) = 36 km/h
• Final velocity (v) = 90 km/h
• Time taken (t) = 5 seconds

We've been asked to calculate acceleration.

In order to calculate the acceleration in its SI unit, firstly we need to convert velocities into their SI units. SI unit of velocity is m/s. So, we need to convert km/h to m/s. In order to convert km/h to m/s, we multiply the value by 5/18.

$\large {\underline { \sf {Initial \; velocity \; in \; m \: s^{-1} :}}}$

$\implies\sf{u = 36 \; km \: h^{-1}}$

$\implies\sf{u = \Bigg ( \cancel{36} \times \dfrac{5}{\cancel{18}} \Bigg ) \;m \: s^{-1} }$

$\implies\sf{u = \Bigg ( 2 \times 5 \Bigg ) \; m \: s^{-1} }$

$\implies \boxed{\sf{u =10 \; m \: s^{-1} }} \dots \; \bf ( 1 )$

$\rule{200}2$

$\large {\underline { \sf {Final \; velocity \; in \; m \: s^{-1} :}}}$

$\implies\sf{v = 90 \; km \: h^{-1}}$

$\implies\sf{v = \Bigg ( \cancel{90} \times \dfrac{5}{\cancel{18}} \Bigg ) \;m \: s^{-1} }$

$\implies\sf{v = \Bigg ( 5 \times 5 \Bigg ) \; m \: s^{-1} }$

$\implies \boxed{\sf{v = 25\; m \: s^{-1} }} \dots \; \bf ( 2 )$

$\rule{200}2$

Now, we'll find tha acceleration. Acceleration can be calculated using the first equation of motion,

$\implies\sf{v = u + at }$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time

Substitute the values of velocities from ( 1 ) and ( 2 ) and the given information.

$\implies\sf{25 = 10 + 5a}$

$\implies\sf{25 - 10 = 5a}$

$\implies\sf{15 =5a}$

$\implies\sf{\cancel{\dfrac{15}{5}}= a}$

$\implies\boxed{\red{\sf{3 \; m \: s^{-2} = a}}}$

∴ The acceleration of the scooter is 3 m/s².