Question

If a body travels for time ' t ' with speed v₁ and then it further travels for time ' t ' with speed v₂, 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.

So speed = $\frac{\text{distance}}{\text{time}}$

From this, the formula for distance will be

$\text{distance =speed×time.}$

2. Average speed of a body can be calculated by dividing the total distance traveled by the body by the total time taken by the body.

So average speed =$\frac{totaldis\tan ce}{totaltime}$.

Step 2: Calculating average speed

1. let d₁ be the distance traveled by the body with speed v₁ in time interval t and d₂ be the distance traveled by the body with speed v₂ in time interval t. So here $d_1=v_1\times t$ and$d_2=v_2\times t$

2. Now average speed =$\frac{totaldis\tan ce}{totaltime}$= $\frac{d_1+d_2}{t+t}$= $\frac{v_{1}t+v_{2}t}{2t}$ = $\frac{t(v_1+v_2)}{2t}$=$\frac{v_1+v_2}{2}$

Hence, average speed =$\frac{v_1+v_2}{2}$.