At t = 0, a particle starts at rest and moves along a line in such a way that, at time t, its acceleration is 24t 2 ft / s2. through how many feet does the particle move during the first 2 seconds?

The distance in feet covered by this particle during the first 2 seconds is 32 feet.

Given the following data:

To calculate the distance in feet covered by this particle during the first 2 seconds:

First of all, we would determine the velocity at which the particle is moving by integrating the value of its acceleration as follows;

Next, we would calculate the position of this particle by integrating the velocity with respect to time;

Now, we can calculate the distance covered by this particle during the first 2 seconds:

Distance = 32 feet.

Read more on distance here: link

the force on the thing and the distance the force moves the thing