The equation of motion is s = 6 cos(t) + 4 sin(t), t >= 0, where s is measured in centimeters and t in seconds. (Take the positive direction to be downward.) (a) Find the velocity and acceleration at time t. v(t) = a(t) =
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Given the position function: \[ s(t) = 6 \cos(t) + 4 \sin(t) \] To find the velocity, we differentiate \( s(t) \) with respect to \( t \): \[ v(t) = \frac{d}{dt} (6 \cos(t) + 4 \sin(t)) \] Using the derivatives of cosine and sine functions: \[ \frac{d}{dt} Show more…
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