Question

A car increases its speed with uniform rate from 20 km/h to 50 km/h in 10 seconds, average speed of car is

(1) 35 km/h

(2) 40 km/h

(3) 45 km/h

(4) 30 km/h​

Answer 1

Given : A car increases its speed with uniform rate from 20 km/h to 50 km/h in 10 seconds,

To Find : average speed of car

(1) 35 km/h

(2) 40 km/h

(3) 45 km/h

(4) 30 km/h​

Solution:

u = Initial velocity = 20 km/h

v = final velocity = 50 km/h

Speed increases uniformly hence

average speed of car = (u + v)/2

= ( 20 + 50)/2

= 35 km /h

Additional Info

acceleration = ( v- u ) / t

v -  u = 50 - 20  = 30 km /h  = 30 * 5/18  m/s

= 25/3  m/s

acceleration =  (25/3)/10 = 25/30

= 5/6  m/s²

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Answer 2

Given:

A car increases its speed with uniform rate from 20 km/h to 50 km/h in 10 seconds.

To find:

Average Speed of car?

Calculation:

USE v_(avg) = (u+v)/2 directly ONLY IN MCQs, NOT IN SCHOOL/BOARD EXAMS !!

FOR SCHOOL EXAMS, follow this method:

$\rm v_{avg} = \dfrac{displacement}{time}$

$\rm \implies \: v_{avg} = \dfrac{s}{t}$

$\rm \implies \: v_{avg} = \dfrac{ut + \dfrac{1}{2}a {t}^{2} }{t}$

$\rm \implies \: v_{avg} = u + \dfrac{1}{2}a t$

$\rm \implies \: v_{avg} = \dfrac{2u + at}{2}$

$\rm \implies \: v_{avg} = \dfrac{u + (u + at)}{2}$

$\rm \implies \: v_{avg} = \dfrac{u + v}{2}$

AFTER THIS DERIVATION, you can put the values:

$\rm \implies \: v_{avg} = \dfrac{20 + 50}{2}$

$\rm \implies \: v_{avg} = \dfrac{70}{2}$

$\rm \implies \: v_{avg} = 35 \: km/hr$

So, average velocity is 35 km/hr.