# A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration?

## a = vf - vi t

Aug 3, 2017

$\text{acceleration} = 7.33$ $\text{m/s}$

#### Explanation:

We're asked to find the (constant) acceleration of the roller coaster, given its final and initial velocities.

To do this, we can use the kinematics equation

ul(v_x = v_(0x) + a_xt

where

• ${v}_{x}$ is the final velocity

• ${v}_{0 x}$ is the initial velocity

• ${a}_{x}$ is the acceleration (what we're trying to find)

• $t$ is the time interval

We know:

• ${v}_{x} = 32$ $\text{m/s}$

• ${v}_{0 x} = 10$ $\text{m/s}$

• a_x = ?

• $t = 3$ $\text{s}$

Plugging in known values:

$32$ $\text{m/s}$ $= 10$ $\text{m/s}$ $+ {a}_{x} \left(3 \textcolor{w h i t e}{l} \text{s}\right)$

a_x = (32color(white)(l)"m/s" - 10color(white)(l)"m/s")/(3color(white)(l)"s") = color(red)(ulbar(|stackrel(" ")(" "7.33color(white)(l)"m/s"^2" ")|)