The equation of motion of a particle is $s = t^3 - 12t$, where s is in meters and t is in seconds. (Assume $t \ge 0$.) (a) Find the velocity and acceleration as functions of t. v(t) = a(t) = (b) Find the acceleration after 3 s. m/s$^2$ (c) Find the acceleration when the velocity is 0. m/s$^2$
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To find the velocity, we need to take the derivative of the equation of motion with respect to time. Given: s = 3 - 12t Taking the derivative of s with respect to t, we get: v(t) = d/dt (3 - 12t) v(t) = -12 So, the velocity as a function of t is v(t) = -12. Show more…
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