Question

A ball rolls down a ramp for 15 seconds. If the initial velocity of the ball was 0.8 m/s and the final velocity was 7 m/s, what was the acceleration of the ball?

Answer 1

`a_x = 0.41` `"m/s"^2`

Explanation:

We're asked to find the (constant) acceleration of a ball as it rolls down a ramp, given its initial and final velocities, and the time interval.

To do this, we can use the equation

`v_x = v_(0x) + a_xt`

where

• `v_x` is the final velocity (`7` `"m/s"`)

• `v_(0x)` is the initial velocity (`0.8` `"m/s"`)

• `a_x` is the constant acceleration (what we're trying to find)

• `t` is the time interval (`15` `"s"`)

Plugging in known values, we have

`7` `"m/s"` `= 0.8` `"m/s"` `+ a_x(15color(white)(l)"s")`

`a_x = (7color(white)(l)"m/s" - 0.8color(white)(l)"m/s")/(15color(white)(l)"s") = color(red)(ul(0.41color(white)(l)"m/s"^2`

rounded to `2` significant figures.