Question

If a body travels with speeds v₁, v_2, and v₃ for equal intervals of time, find the average speed.

Answer 1

Step 1: Definition of speed, average speed

1. The rate of change of distance with respect to time is called speed.
2. So $speed=\frac{distance}{time}$.
3. From this $\text{distance = speed×time}$
4. The average speed is calculated by dividing the total distance traveled by a body by the total time taken by the body.

$Averagespeed=\frac{Totaldis\tan cetraveled}{Totaltimetaken}$

Step 2: Calculation of average speed

1. Let ‘t’ is the time interval d₁, d₂ and d₃ are the distances traveled by the body in three equal intervals.

And v₁, v_2, v₃ are the speed of the body in three equal intervals.

So as per the definition of speed, $d_2=v_{2}t$ and $d_3=v_{3}t$

2. Now average speed = $\frac{d_1+d_2+d_3}{t+t+t}$= $\frac{v_{1}t+v_{2}t+v_{3}t}{3t}$= $\frac{t(v_1+v_2+v_3)}{3t}$= $\frac{v_1+v_2+v_3}{3}$

Thus, the average speed is $\frac{v_1+v_2+v_3}{3}$.