Question

two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

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Rasheed

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57 Answers

Find the equations for the velocities of both particles.
v_1=x_1^{\prime}=\frac{\differentialD}{\differentialD t}\left(\cos\left(t\right)\right),
v_1=-\sin\left(t\right)
v_2=x_2^{\prime}=\frac{\differentialD}{\differentialD t}\left(\exponentialE^{-3t}+1\right)=-3\left(\exponentialE^{-3t}\right)+0,
v_2=-3\exponentialE^{-3t}
Now, let v1 = v2.
v_1=v_2,
-\sin\left(t\right)=-3\exponentialE^{-3t},
\sin\left(t\right)=3\exponentialE^{-3t},
\sin\left(t\right)-3\exponentialE^{-3t}=0
Then, find the values of t, from 0 to 10, as separated by commas.
t=0.5712,3.1414,6.2832,9.4248

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