Question

problem
acceleration describe a balls motion as it rolls up a slanted driveway. it starts with an initial velocity of 1.25 m/s up the ramp. it travels upward, while slowing down, for 4.22 s, stops for an instant, and then rolls back down. what are the direction and the magnitude of the balls acceleration as it rolls up the driveway?

1. analyze and sketch the problem

set up the coordinate system choose the positive direction to be up the driveway. place the origin where the motion begins.
knowns
unknown
v_i=
=?
v_f=
at t=

1. solve for the unknown

solve for the change in velocity and the time taken to make that change.
use the definition of acceleration.

Explanation:

Step1: Identify known values

$v_i = 125\ m/s$ (initial velocity), $v_f=0\ m/s$ (final velocity when it stops), $t = 4.22\ s$ (time taken)

Step2: Use acceleration formula

The formula for acceleration is $a=\frac{v_f - v_i}{t}$. Substitute the known values: $a=\frac{0 - 125}{4.22}$.

Step3: Calculate acceleration

$a=\frac{- 125}{4.22}\approx - 29.62\ m/s^2$. The negative sign indicates the direction is down - the driveway.

Answer:

The magnitude of the acceleration is approximately $29.62\ m/s^2$ and the direction is down the driveway.