Question

A car travels equal distances in the same direction with velocities of $60km/h,20km/h,and10km/h$ respectively. The average velocity of the car over the whole journey is

• A. 5m/s
• B. 6m/s
• C. 7m/s
• D. 8m/s

Answer 1

The correct option is A

5m/s

Step 1: Given data:

1. A car travels equal distances in the same direction.
2. Velocities of the car are $60km/h,20km/h,and10km/h$ respectively.

Let the total distance traveled be 3s km, and let t₁, t_2, and t₃ be the time taken to travel the three distances respectively, and t be the total time taken.

Step 2: Calculating t₁, t_2, and t₃:

$Time=\frac{Dis\tan ce}{Velocity}$

$$\begin{gathered} t_1=\frac{s}{60}hr \\ {t}_2=\frac{s}{20}hr \\ {t}_3=\frac{s}{10}hr \\ Also,t=t_1+t_2+t_3=\frac{s}{60}+\frac{s}{20}+\frac{s}{10} \\ Averagevelocity=\frac{Totaldisplacement}{Totaltimetaken} \\ Therefore,averagevelocity\left(v\right)=\frac{3s}{t}km/hr \end{gathered}$$

Step 3: Calculating average velocity:

$$\begin{gathered} Averagevelocity\left(v\right)=\frac{3s}{t}km/hr \\ v=\frac{3s}{t_1+t_2+t_3} \\ v=\frac{3s}{s/60+s/20+s/10} \\ v=\frac{3s\times 60}{s(1+3+6)} \\ v=18km/hr \\ v=5m/s \end{gathered}$$

Therefore the average velocity is 5 m/s.

Hence, the correct option is (A).