Question

Questions
a ball rolls 3.2m up a constant slope before it comes to a stop if the initial velocity of the ball was 2.2m/s what is the acceleration of the ball as it rolls

Answer 1

To find the acceleration of the ball as it rolls up the slope, we first need to determine the final velocity when the ball comes to a stop at the end of the 3.2m distance.

Using the kinematic equation:
v_f^2 = v_i^2 + 2ad

Where:
v_f = final velocity (0 m/s at the top of the slope)
v_i = initial velocity (2.2 m/s)
a = acceleration (unknown)
d = distance (3.2m)

Plugging in the values:
0 = (2.2)^2 + 2a(3.2)
0 = 4.84 + 6.4a
-4.84 = 6.4a
a = -0.75 m/s^2

Therefore, the acceleration of the ball as it rolls up the slope is -0.75 m/s^2. The negative sign indicates that the acceleration is in the opposite direction of the motion.