# Average velocity – problems and solutions

1. Someone rounds a rectangle with a length of 400 m and width of 100 m, 12 times in 1 hour. What are the average velocity and the average speed?

__Known :__

Length of rectangle = 400 meters

Width of rectangle = 100 meters

Circumference of the rectangle = (2 x 400 meters) + (2 x 100 meters) = 800 meters + 200 meters = 1000 meters

Distance = 12 x 1000 meters = 12,000 meters = 12 kilometers

__Wanted :__ The average velocity and the average speed

__Solution :__

The average velocity :

The person return to the initial velocity after rounds rectangle, hence displacement of the person is 0 and the average velocity is 0.

The average speed :

The average speed = total distance / time interval = 12 km / 1 hour = 12 km/hour

2. The connection between the distance (d) and time interval (t) of a moving object shown in the figure below. If the distance in meter and time in second, what is the average velocity.

Solution

The average speed = distance / time interval

The average velocity = 15 meters / 6 seconds = 2.5 meters/second

3. A bird flies towards the North at 16 m/s in 5 second and then towards the East at 12 m/s in 5 seconds. What is the average velocity for 10 seconds.

Solution :

__The velocity of bird towards the north : 16 meters/second = 16 meters / 1 second__

After 1 second, bird moves as far as 16 meters

After 2 seconds, bird moves as far as 2 x 16 = 32 meters

After 5 seconds, bird moves as far as 5 x 16 = 80 meters

__The velocity of bird towards the east : 12 meters/second = 12 meters / 1 second__

After 1 second, bird moves as far as 12 meter

After 2 seconds, bird moves as far as 2 x 12 = 24 meters

After 5 seconds, bird moves as far as 5 x 12 = 60 meters

__Displacement (s) :__

s = √80^{2} + 60^{2}

s = √6400 + 3600

s = √10,000

s = 100 meters

__The average velocity (v) :__

v = displacement / time

v = 100 meters / 10 seconds

v = 10 meters/second