Question

A football player runs from his own goal line to the opposing team's goal line, returning to his thirty-yard line, all in 25.5 s. Calculate his average speed and the magnitude of his average velocity. (Enter your answers in yards/s.)

HINT

(a)

Calculate his average speed.

yards/s

(b)

Calculate the magnitude of his average velocity.

yards/s

Answer 1

Answer 2

Let's assume that the distance from one goal line to the other is 100 yards, and that the distance from the goal line to the thirty-yard line is 70 yards.

The total distance covered by the football player is twice the distance from one goal line to the thirty-yard line plus the distance from the thirty-yard line to the other goal line:

d = 2(70 yards) + 100 yards = 240 yards

The time it took for the football player to cover this distance is 25.5 s.

(a) The average speed of the football player is the total distance covered divided by the time taken:

average speed = total distance / time taken = 240 yards / 25.5 s ≈ 9.41 yards/s

(b) The average velocity of the football player is the displacement (change in position) divided by the time taken. Since the football player ended up at the same position where he started, his displacement is zero.

Therefore, the magnitude of the average velocity is zero yards/s. Note that the football player's average velocity is zero even though his average speed is not zero. This is because velocity takes into account the direction of motion, whereas speed only considers the magnitude of the motion.