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
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
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
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.