Question 1035774: Please help me with this problem:
The acceleration for a particle moving along the x-axis is a(t) =  . The velocity when t = 0 is 5, and the position of the particle when t = 0 is 2. Develop the velocity function and the position function of the particle. Find the total distance the particle travels during the time interval[0,5].
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! d^2s/dt^2=4e^4t
ds/dt=e^4t+C1; t=0, ds/dt=5, or C1=4, since e^0=1;
v=ds/dt=e^4t+4
therefore,
s=(1/4)e^4t+4t+C; if t=0, s=2; 2=(1/4)+C, and C=7/4
s=(1/4e^(4t)+4t+7/4
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when t=5, position is (1/4)e^20+20+(7/4), and the distance is 121,291,318.6, subtracting the 2 at the end for the initial position.
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