Atrain moving west with an initial velocity of 20 m/s accelerates at 4m/s^2 for 10 seconds. during this time, the train moves a distance of

Explanation:

Now from how I have learned it, we integrate straight from Newton's second law F=ma.

Here we are setting up the problem by writing down F=ma, and then setting it equal to our problem, I used α for the acceleration given in the problem. Next, we integrate from a = α to vf = αt + vi, where vf is the final velocity, vi is the initial velocity, α is our problem's acceleration, and t is our total time. We then proceed to integrate again from that to xf = αt^2/2 + vit + xi where xf is our final position, and xi is our starting position. For the problem we can say that he started from 0m, so the xi = 0m. After plugging in our values we do some algebra to solve for xf, which turns out to be 400m.

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas