Movement of a Particle

[JaysFanatic]

Hi.

I believe I did this problem right but I'm not sure if i got the correct answer.

The acceleration of a particle moving along a straight line is given by a=10e^2t.

During the time when velocity increases from 5 to 15, how far does the particle travel?

I figured out from other parts of the problem that the derivative was v(t) = 5e^2t, so i figured out that when v= 5 t=0 and v=15 t= ln(3)/2. Then I used the antiderivative of that function (a=10e^2t) from 0 to (ln3)/2 to come up with Integrate from 0 to (ln3)/2 for 10e^2t. I got an answer of 20. Is that right?

 

[JaysFanatic]

Actually i think it might be 5 my bad.

 

[galactus]

Yes, I get 5 as well.

\(\displaystyle \int 5e^{2t}dt=\frac{5}{2}e^{2t}\)

Using t=0 and t=ln(3)/2 gives \(\displaystyle \frac{15}{2}-\frac{5}{2}=5\)