Question

A car travels along a straight line for first half time with speed $40km/hr$ and the second half time with speed $60km/hr$. Find the average speed of car.

Answer 1

Step 1: Given

Speed during the first half, $v_1=40km/hr$

Speed during the second half, $v_2=60km/hr$

The total time taken is $T$

Step 2: Formula used

1. $Dis\tan ce=Speed\times time$
2. $Averagespeed=\frac{Totaldis\tan ce}{Totaltime}$

Step 3: Calculate the distance covered in the first half

The time during the first half will be $\frac{t}{2}$

$$\begin{gathered} Dis\tan ce=Speed\times time \\ =v_1\times \frac{t}{2} \\ =40\times \frac{t}{2} \\ =20tkm \end{gathered}$$

Step 4: Calculate the distance covered in the second half

The time during the second half will be $\frac{t}{2}$

$$\begin{gathered} Dis\tan ce=Speed\times time \\ =v_1\times \frac{t}{2} \\ =60\times \frac{t}{2} \\ =30tkm \end{gathered}$$

Step 5: Calculate the average speed

$$\begin{gathered} Averagespeed=\frac{Totaldis\tan ce}{Totaltime} \\ =\frac{20t+30t}{T} \\ =\frac{20t+30t}{{\displaystyle \frac{t}{2}}+{\displaystyle \frac{t}{2}}} \\ =\frac{50t}{t} \\ =50km/hr \end{gathered}$$

Therefore, the average speed of the car is $50km/hr$.