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 $t = 3$ ?

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Answer 1 · 2017-08-11T00:58:38

$v=42 " units"$

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 $42" units."$

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