The equation of motion of a particle is s = t3 − 3t

Algebra
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The equation of motion of a particle is  s = t3 − 3t,  s is in meters and t is in seconds. (Assume t =/> 0)

1- Find the velocity and acceleration as functions of t.

2-  Find the acceleration after 4 s.

3- Find the acceleration when the velocity is 0.

May 6th, 2015

1. the velocity v(t) = ds/dt = 3t^2 - 3 

acceleration a(t) = dv/dt = 6*t

2. a(4)=6*4=24 m/s^2

3. v = 0 = 3t^2 - 3 

3t^2=3
t^2 = 3/3 
t^2 = 1 
t=+1 
t = - 1 has no meaning. 
at t=1 the acceleration is a(1) = 6*1 = 6 m/s^2

May 6th, 2015

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