A football player carrying the ball runs straight ahead at the line of scrimmage and directly into a wall of defensive linemen. The ball carrier has an initial speed of 8.48 m/s and is stopped in a time interval of 0.186 s. Find the magnitude and direction of his average acceleration.

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To find the magnitude of the ball carrier's average acceleration, we can use the following equation:

acceleration = (final velocity - initial velocity) / time

In this case, the ball carrier's final velocity is 0 m/s since he is stopped, the initial velocity is 8.48 m/s, and the time interval is 0.186 s. Plugging in these values, we get:

acceleration = (0 - 8.48) / 0.186
acceleration = -8.48 / 0.186
acceleration ≈ -45.51 m/s²

So, the magnitude of the ball carrier's average acceleration is approximately 45.51 m/s².

To find the direction of the average acceleration, we need to consider that the ball carrier is running straight ahead and directly into a wall of defensive linemen. Since the ball carrier's initial velocity is positive (he is running forward), and the final velocity is 0 m/s (he is stopped), we can conclude that the average acceleration is in the opposite direction of his initial velocity. Therefore, the direction of the average acceleration is "backward" or "opposite to his forward motion."

To find the magnitude and direction of the average acceleration, we first need to determine the change in velocity.

The change in velocity can be calculated using the formula:
Δv = vf - vi
where vf is the final velocity and vi is the initial velocity.

In this scenario, the ball carrier is stopped, so the final velocity (vf) is 0 m/s.

Δv = 0 - 8.48 m/s
Δv = -8.48 m/s

Now, we can calculate the average acceleration using the formula:
a = Δv / t
where a is the average acceleration and t is the time interval.

a = -8.48 m/s / 0.186 s
a ≈ -45.48 m/s²

The magnitude of his average acceleration is approximately 45.48 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial motion.

Therefore, the magnitude of the average acceleration is 45.48 m/s², and its direction is opposite to the initial motion of the football player.