1. The Problem
The acceleration function for a particle is given as a(t)=60t+18. v(1)=5, find the distance traveled by the particle from t=0 to t=2
3. The attempt at a solution
First, I integrated the acceleration function to get the velocity function, I found:
v(t)=30t2+18t+c
v(1)=5=30+18+C
5=48+C
C=-43
So v(t)=30t2+18t-43
Well, now I scratched my head a little bit. I know that the distance traveled is the absolute value of the integral of this function on my interval, but with the -43 hanging out on the end of this equation, I will not be able to factor. I approached my prof. about this and he said there was a formula that I should use, and that the quadratic equation solution that I produced wasn't necessary, and that this problem could be done on a scientific calculator.
What am I missing?
(I had hoped that v(1) would be 0 so it would split right down the middle :cry: )
TIA for the help.
Chris
The acceleration function for a particle is given as a(t)=60t+18. v(1)=5, find the distance traveled by the particle from t=0 to t=2
3. The attempt at a solution
First, I integrated the acceleration function to get the velocity function, I found:
v(t)=30t2+18t+c
v(1)=5=30+18+C
5=48+C
C=-43
So v(t)=30t2+18t-43
Well, now I scratched my head a little bit. I know that the distance traveled is the absolute value of the integral of this function on my interval, but with the -43 hanging out on the end of this equation, I will not be able to factor. I approached my prof. about this and he said there was a formula that I should use, and that the quadratic equation solution that I produced wasn't necessary, and that this problem could be done on a scientific calculator.
What am I missing?
(I had hoped that v(1) would be 0 so it would split right down the middle :cry: )
TIA for the help.
Chris
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