Please check my work on this short calc (?) prob

[frasifrasi]

Homework Statement

Two particles move along an x axis. Position of particle 1 is x = 6t^2 + 3t + 2. The acceleration of particle 2 is given by a = -8t and at t=0, its velocity is 20 m/s. When the velocities of the particles match, what is their velocity?

Homework Equations

The Attempt at a Solution

Ok, so I took the derivative of the position function and found it to be v = 12t + 3. Then I took the integral from the acceleration function and found it to be v = -4t^2 + C ( by plugging t=0, I got C = 20). Hence, v = -4t^2 + 20.

Now, I equated both velocity functions and was left with 4t^2 + 12t -17. Does that mean I should solve the quadratic to get two answers--this seems too simple and the problem is supposed to be 3/3 for difficulty...

 

[rootX]

Homework Statement

Two particles move along an x axis. Position of particle 1 is x = 6t^2 + 3t + 2. The acceleration of particle 2 is given by a = -8t and at t=0, its velocity is 20 m/s. When the velocities of the particles match, what is their velocity?

Homework Equations

The Attempt at a Solution

Ok, so I took the derivative of the position function and found it to be v = 12t + 3. Then I took the integral from the acceleration function and found it to be v = -4t^2 + C ( by plugging t=0, I got C = 20). Hence, v = -4t^2 + 20.

Now, I equated both velocity functions and was left with 4t^2 + 12t -17. Does that mean I should solve the quadratic to get two answers--this seems too simple and the problem is supposed to be 3/3 for difficulty...

yes, that's what I did also, before reading yours work.

 

[Doc Al]

Your work looks right to me.

 

[frasifrasi]

Thank you, but how is it that you come out with two aswers? Should I eliminate the negative one or is it physically possible in this case?

 

[rootX]

because it's quadratic v = -4t^2 + 20

why you hate negative value lol?
how's it different from positive?