physics: Instantaneous speed versus average speed?
Instantaneous speed versus average speed
1.) Speed is the magnitude of instantaneous velocity. Is the average speed equal to the magnitude of the average velocity? Justify your answer.
2.) Under what condition is the average equal to instantaneous velocity?
3.) A car travels at 40mph for 2hr and 60mph for 3hr. what is its average speed.
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Verified answer
1) Average speed is not equal to the magnitude of average velocity.
For example, if a marathon runner finishes a 40km marathon in, say 5h, his average velocity is 0 kph, because < v > = (xf - xi) / (tf - ti), and since xf = xi (his final position xf is equal to his initial position xi), his average velocity is 0 kph.
His average speed, however, is total distance (40 km) divided by total time taken (5h), which is 8 kph.
2) Average velocity is equal to instantaneous velocity only if the object moves with constant velocity during the entire motion.
3) average speed = total distance / total time
= [(40 mph × 2 h) + (60 mph × 3 h)] / (2 h + 3 h)
= (80 mi + 180 mi) / 5 h
= 52 mph
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