Jamari Bowman

2023-02-21

The position of an object moving along a line is given by . What is the speed of the object at ?

Bobby Espinoza

Solution
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:
$p\left(t\right)=2{t}^{3}-2{t}^{2}+1$
$⇒p\prime \left(t\right)=v\left(t\right)=6{t}^{2}-4t$
At t=3, we have:
$v\left(t\right)=6{\left(3\right)}^{2}-4\left(3\right)$
$=54-12$
$=42$
At t=3, the object has a speed of 42 units.

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