Question

A 3.6 kg box is traveling at 8.5 m/s just before it hits a pillow. It takes 1.2 s for the box to stop. How much will the box accelerate from hitting the pillow?

Answer 1

`\sf 7.083 \, \text{m/s}^2`

Step-by-step explanation:

To determine the acceleration of the box, we can use the kinematic equation that relates initial velocity
`\sf (v_0)`, final velocity (v), acceleration (a), and time (t):

`\sf v = v_0 + at`

In this case, the box is coming to a stop, so the final velocity (v) is 0 m/s. The initial velocity
`\sf (v_0)` is 8.5 m/s, and the time (t) it takes to stop is 1.2 seconds.

The equation becomes:

`\sf 0 = 8.5 + a \cdot 1.2`

Now, solve for (a):

`\sf a = (-8.5)/(1.2)`

`\sf a \approx -7.083 \, \text{m/s}^2`

The negative sign indicates that the acceleration is in the opposite direction to the initial velocity.

Therefore, the box decelerates (slows down) at a rate of approximately
`\sf 7.083 \, \text{m/s}^2` when it hits the pillow.