Question

A car travelling along a straight line traversed one-half of the total distance with a velocity 30 km/h. The remaining part of the distance was covered with a velocity 20 km/h, for half of the time and with velocity 40 km/h for the other half of time. The mean velocity averaged over the whole time of motion is

Answer 1

Answer:

30 Km/hr

Explanation:

Let total distance d

Let time covered for first one third distance be t1

t1= d/3/30

  =d/90

let the time for travelling remaining distance be t2

d−  d /3=2d/3 =2*t2 +6*t2 =8*t  2

avg speed on t2 is equal to t1

t2=t1

t2=d/90

avg velocity = total dist

                       total time

v =      d          

      t1+2*t2

v =        d      

​  d+    2d  

       90    90

v= 30 km/hr

Answer 2

Given:

A car travelling along a straight line traversed one-half of the total distance with a velocity 30 km/h. The remaining part of the distance was covered with a velocity 20 km/h, for half of the time and with velocity 40 km/h for the other half of time.

To find:

Average Velocity for whole journey.

Calculation:

First we will calculate the average Velocity for 2nd half of journey. Since the 2nd half was travelled with 20 km/hr and 40 km/hr in equal times.

$avg. \: v = \dfrac{20 + 40}{2} = 30 \: km {hr}^{ - 1}$

Now , the whole journey involved the car travelling with 30 km/hr for 1st half distance and then again at 30 km/hr for the rest half.

$avg. \: v_{final} = \dfrac{2 \times (30 \times 30)}{30 + 30}$

$= > avg. \: v_{final} = \dfrac{2 \times (30 \times 30)}{60}$

$= > avg. \: v_{final} = \dfrac{30 \times 30}{30}$

$= > avg. \: v_{final} = 30 \: km {hr}^{ - 1}$

So , final answer is:

$\boxed{ \bf{avg. \: v_{final} = 30 \: km {hr}^{ - 1} }}$

Important formulas that can be used in competitive exams:

• For equal time , avg v = (v1+v2)/2

• For equal distance avg v = 2v1v2/(v1+v2)