Logistics help

[ayu24]

Hey guys, I am having some trouble with some calculus problems that I have for homework and I would like some help. If you guys choose to help answer my questions, would you mind posting the steps that you took in solving them as well?

An object initially at rest at (3,3) moves with acceleration a(t)=(2,e^-t). Where is the object at t=2?

After t years, 50e^-.015t pounds of a deposit of radioactive substance remains. The average amount per year NOT lost by radioactive decay during the second hundred years is?

A particle moves along a line with an acceleration a=6t. If, when t=0, v=1, then the total distance traveled between t=0 and t=3 equals?

Thanks in advance for the help!

 

[tkhunny]

Most appropriately, you would show us YOUR work. It this way, you could take credit for doing your own homework.

Let's see your efforts.

You should know these:

Location: x(t)

Speed/Velocity: v(t) = (d/dt)x(t)

Acceleration: a(t) = (d/dt)v(t)

 

[ayu24]

Well, I really had no idea on how to solve them, which is why I asked for you to show me how to do the problem.

 

[tkhunny]

What you are saying is that you have not ever attended class, haven't once opened your book, nor have you done anything else that may contribute to your education. No one can help you as long as this is the effort you have to offer.

Come on. Throw me a bone. Do the x-direction first. That's a nice constant acceleration. Use the three equations I gave you (which you should have already), and let's see what you get.

x(0) = 3

 

[craigafriedman]

Solution

The average amount not lost is the same as the average amount remaining from 100 to 200 years, where the amount remaining is 50e^-0.015t. To find the "average" of anything in calculus, like 50e^-0.015t, integrate 50e^-0.015t (from 100 to 200 years) and then divide by the length of the interval, 200-100, which comes out to 5.778

Hey guys, I am having some trouble with some calculus problems that I have for homework and I would like some help. If you guys choose to help answer my questions, would you mind posting the steps that you took in solving them as well?

An object initially at rest at (3,3) moves with acceleration a(t)=(2,e^-t). Where is the object at t=2?

After t years, 50e^-.015t pounds of a deposit of radioactive substance remains. The average amount per year NOT lost by radioactive decay during the second hundred years is?

A particle moves along a line with an acceleration a=6t. If, when t=0, v=1, then the total distance traveled between t=0 and t=3 equals?

Thanks in advance for the help!