Question

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

Answer 1

`"acceleration" = 7.33` `"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_(0x)` 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` `"m/s"`

• `v_(0x) = 10` `"m/s"`

• `a_x = ?`

• `t = 3` `"s"`

Plugging in known values:

`32` `"m/s"` `= 10` `"m/s"` `+ a_x(3color(white)(l)"s")`

`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" ")|)`