Question

set up the coordinate system. choose the positive direction to be up the driveway. place the origin where the motion begins.
knowns
unknown
$v_i = 1.25$
$a=\frac{v_f - v_i}{t}=$?
$v_f = 0$ at $t = 4.22$

1. solve for the unknown

solve for the change in velocity and the time taken to make that change.
$a=-1.25 / 4.22=-0.296\\ m/s^2$
use the definition of acceleration.
the magnitude of the acceleration is approximately $0.296\\ m/s^2$ and the direction is down the driveway (since the value is negative and we defined up the driveway as positive).

1. evaluate the answer

. are the units correct?
. do the directions make sense?

Explanation:

Step1: Identify acceleration formula

The formula for acceleration is $a=\frac{v_f - v_i}{t}$, where $v_i$ is the initial - velocity, $v_f$ is the final - velocity, and $t$ is the time.

Step2: Substitute known values

Given $v_i = 1.25\ m/s$, $v_f=0\ m/s$, and $t = 4.22\ s$. Substitute into the formula: $a=\frac{0 - 1.25}{4.22}$.

Step3: Calculate acceleration

$a=\frac{- 1.25}{4.22}\approx - 0.296\ m/s^2$. The negative sign indicates the direction is opposite to the positive direction (up - the driveway as defined).

Answer:

The acceleration is approximately $-0.296\ m/s^2$.