Question

A car moves towards north at a speed of 54 km/h for 1 h. Then it moves eastward with same speed for same duration. The average speed and average velocity of car for complete journey is :

• A. $54km/h,0$
• B. $15m/s,\frac{15}{\sqrt{2}}m/s$
• C. $0,0$
• D. $0,\frac{54}{\sqrt{2}}km/h$

Answer 1

The correct option is B $15m/s,\frac{15}{\sqrt{2}}m/s$

Average speed is the ratio of the total distance travelled by the car and the total time taken,

$Spee{d}_{avg}=\frac{15t+15t}{t+t}$ ($\because 54km/s=15m/s$)

or, $Spee{d}_{avg}=15m/s$

Average velocity will be the ratio of displacement and time.

The car moves north first and then east. The shortest distance will be the hypotenuse of the triangular path.

$v_{avg}=\frac{15\sqrt{2}t}{t+t}$

or, $v_{avg}=\frac{15\sqrt{2}}{2}$

or, $v_{avg}=\frac{15}{\sqrt{2}}$ is our required answer.

The correct answer is therefore option (B).