# Determine the position, velocity, acceleration, and distance traveled at t=8s?

The position of a particle that moves along the x-axis is given by x=(t^3)-3(t^2)-45t m

where t is the time in seconds.

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• 7 years ago

Position:

Since you're given the equation for position we just plug in the time we want to evaluate it at.

x(8) = (8^3)-3(8^2)-45*8 = -40

Velocity:

Velocity is the change in position over change in time or deltaX/deltaT

This is the slope of the position equation as such we have to take the derivative of it to find velocity.

dx/dt = 3*t^2-3*2*t-45

we then evaluate dx/dt at 8 seconds

dx/dt(8) = 3*64 - 6*8 - 45 = 99 m/s

Acceleration:

Acceleration is the change in velocity over the change of the change in time or a = dv/dt^2

As such we have to take the derivative of the velocity equation and evaluate at time 8 sec.

dx/dt = 3*t^2-3*2*t-45

dv/dt^2 = 3*2*t - 6

evaluated at t = 8

dv/dt^2(8) = 6*8 - 6 = 42

Source(s): Calculus
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