A particle moves in a straight line so that its position at time \( t \) is \( s ( t ) = t ^ { 3 } - 12 t + 3 \) , where \( t \) is measured in seconds and \( s \) is measured in meters. a) Find the velocity function \( v ( t ) \) . b) When is the particle moving forward and when is it moving backward? d) Find the acceleration function \( a ( t ) \) . e) When is the particle speeding up? When is it slowing down?
Pregunta
Answer
a) \(v(t)=3t^2-12\)
b) forward: \(v(t)>0\Rightarrow t>2\)
backward: \(v(t)<0\Rightarrow 0<t<2\)
c) \(d=|s(3)-s(0)|=9\)
d) \(a(t)=v'(t)=6t\)
e) \(t>0\Rightarrow a(t)>0\Rightarrow\)always speeding up
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