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# Is the velocity of the particle constant or changing?

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The position of a particle moving on an x axis is given by: x=7.8 + 9.2t - 2.1t^3 with x in meters and t in seconds. What is its velocity at t=3.5s? Is velocity constant or changing?

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This solution provides step by step calculations for finding the velocity based on the derivative of 'x' with respect to 't'.

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Velocity = rate of change in displacement/change in time

v = dx/dt which is the derivative of 'x' with respect to 't'

= d(7.8+9.2t-2.1t^3)/dt

= d(7.8)/dt + d(9.2t)/dt - d(2.1t^3)/dt

since d(a+b+c)/dt = ...

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