# Maria is painting the trim on the top of a building. She drops her paintbrush. The paintbrush has a velocity of 29.4 m/s when it hits the ground 3 s later. What is the acceleration of the paintbrush?

May 26, 2017

$a = 9.8 \frac{m}{s} ^ 2$

#### Explanation:

Use the formula $a = \frac{{v}_{f} - {v}_{i}}{{t}_{f} - {t}_{i}}$ where $a$ is the acceleration, ${v}_{f}$ the final velocity, ${v}_{i}$ the initial velocity, $\delta t$ the change in time, which can also be written as ${t}_{f} - {t}_{i}$.

3 seconds later suggests that the change in time was 3 seconds.

The final velocity is 29.4m/s

The initial velocity is 0 because that was the velocity of the paintbrush just as it started its descent.

Therefore,
$a = \frac{29.4 - 0}{3}$
$a = 9.8$

This is the speed of acceleration due to gravity on Earth. Initially, you could've solved it by looking at it but I wanted to give you how to work out answers like this.