Solved Problems in Linear Motion – Average speed and average velocity

1. A car travels along a straight road to the east for 100 meters in 4 seconds, then go the west for 50 meters in 1 second. Determine average speed and average velocity.

Solution

Distance = 100 meters + 50 meters = 150 meters

Displacement = 100 meters – 50 meters = 50 meters, to east.

Time elapsed = 4 seconds + 1 second = 5 seconds.

Average speed = Distance / time elapsed = 150 meters / 5 seconds = 30 meters/second.

Average velocity = Displacement / time elapsed = 50 meters / 5 seconds = 10 meters/second.

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2. A person walks 4 meters east in 1 second, then walks 3 meters north in 1 second. Determine average speed and average velocity.

Solution

__Distance = 4 meters + 3 meters = 7 meters__

Displacement = = meters, to northeast.

Time elapsed = 1 second + 1 second = 2 seconds.

__Average speed = distance / time elapsed = 7 meters / 2 seconds = 3.5 meters/second__

__Average velocity = displacement / time elapsed = 5 meters / 2 seconds = 2.5 meters/second __

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3. A runner travels around rectangle track with length = 50 meters and width = 20 meters. After travels around rectangle track two times, runner back to starting point. If time elapsed = 100 seconds, determine average speed and average velocity.

Solution

Circumference of rectangle = 2(50 meters) + 2(20 meters) = 100 meters + 40 meters = 140 meters.

Travels around rectangle 2 times = 2(140 meters) = 280 meters.

__Distance = 280 meter__.

__Displacement = 0 meter__. (runner back to start point)

Average speed = distance / time elapsed = 280 meters / 100 seconds = 2.8 meters/second.

Average velocity = displacement / time elapsed = 0 / 100 seconds = 0.

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