INITIAL VELOCITY , CALCULUS HELPP!!
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INITIAL VELOCITY , CALCULUS HELPP!!

[From: ] [author: ] [Date: 11-09-28] [Hit: ]
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An object is moving in a straight line such that its position x meters from a fixed point O in the line at any time t seconds is given by x=t^2-6t+8
Find the object's initial velocity

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Find d/dt

x = t^2 - 6t + 8
d/dt(x) = 2t - 6
dx/dt = 2t - 6
velocity = 2t - 6

At t = 0, velocity = -6

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The derivative of position is velocity so taking the derivative of x you get

x'(t) = 2t - 6

The objects initial velocity is at t = 0 so

x'(0) = 2(0) - 6

= -6

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-6 units per second. It is just the coefficient in front of the t.
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