The position of an object moving along a line is given by #p(t) = 2t^3 - 2t^2 +1#. What is the speed of the object at #t = 3 #?

1 Answer
Morgan
Aug 11, 2017

#v=42 " units"#

Explanation:

The speed of an object is the magnitude of the object's velocity , which is the derivative of displacement (magnitude is position).

To find the speed of the object at time #t#, we can begin by taking the derivation of the provided equation for position:

#p(t)=2t^3-2t^2+1#

#=>p'(t)=v(t)=6t^2-4t#

At #t=3#, we have:

#v(t)=6(3)^2-4(3)#

#=54-12#

#=42#

#:.# At #t=3#, the object has a speed of #42" units."#

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