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A particle's position on the x axis is g...

A particle's position on the x axis is given by
`x = 4 - 27 t +t^(3)`,
wth `x` in meters and t in seconds.
(a) Because position x depends on time t, the particle must be moving. Find the particle's velocity function `v(t)` and acceleration function `a(t)`.

Text Solution

AI Generated Solution

To solve the problem, we need to find the velocity and acceleration functions of the particle given its position function \( x(t) = 4 - 27t + t^3 \). ### Step 1: Find the Velocity Function \( v(t) \) The velocity of a particle is defined as the derivative of its position with respect to time. Therefore, we need to differentiate the position function \( x(t) \). Given: \[ x(t) = 4 - 27t + t^3 ...
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