Answer is: option3
5Solution:
The position functions of the two particles are:
\[ x_1(t) = \sin^2 t \]
\[ x_2(t) = e^{-t} \]
Velocity of Particle 1:\[ v_1(t) = \frac{d}{dt} (\sin^2 t) = 2 \sin t \cos t = \sin(2t) \]
Velocity of Particle 2:\[ v_2(t) = \frac{d}{dt} (e^{-t}) = -e^{-t} \]
Solve for \( t \) When \( v_1(t) = v_2(t) \)\[ \sin(2t) = -e^{-t} \]
This equation needs to be solved for \( 0 \leq t \leq 8 \).
The equation has five solutions in the given range.