Question

a basketball is launched to the left with a speed of 5.00 m/s. after hitting a wall, the ball returns on the same line at 4.50 m/s. if the ball was in contact with the wall for 0.310 seconds, find the direction of the average acceleration experienced by the ball during the time of contact? multiple choice negative impossible to determine, since the direction of the force is not given. no sign, since the acceleration is zero. positive

Explanation:

1. Define the initial velocity direction (left) as negative, so \( v_i = - 5.00\space m/s \), and the final velocity (right) as positive, \( v_f = 4.50\space m/s \). The time of contact \( \Delta t = 0.310\space s \).
2. Use the acceleration formula \( a=\frac{\Delta v}{\Delta t}=\frac{v_f - v_i}{\Delta t} \). Substitute the values: \( a=\frac{4.50 - (-5.00)}{0.310}=\frac{9.50}{0.310}\approx30.6\space m/s^2 \)? Wait, no, wait. Wait, no—wait, the direction: Wait, actually, let's re - define. Let's take the initial direction (left) as positive. Then \( v_i = 5.00\space m/s \), \( v_f=-4.50\space m/s \) (since it's moving right, opposite to initial). Then \( a=\frac{v_f - v_i}{\Delta t}=\frac{-4.50 - 5.00}{0.310}=\frac{-9.50}{0.310}\approx - 30.6\space m/s^2 \). The negative sign indicates that the acceleration is in the opposite direction of the initial velocity (i.e., to the right), but when considering the direction relative to the initial motion (left), the acceleration has a negative sign (if initial is positive) or we can see that the velocity change is from left - ward to right - ward, so the acceleration is in the right - ward direction, but in terms of the sign based on the initial velocity direction, it's negative. So the average acceleration has a negative sign (depending on the coordinate system), so the direction of the average acceleration is such that the sign is negative (if we took initial direction as positive). So the answer is Negative.

Answer:

Negative