Motion Along a Line In Exercises 97-100, the function s(f) describes the motion of a particle along a line, (a) Find the velocity function of the particle at any time . (b) Identify the time interval(s) on which the particle is moving in a positive direction, (c) Identify the time inters al(s) on which the particle is moving in a negative direction, (d) Identify the time(s) at which the particle changes direction.
To calculate: The velocity function for the particle if .
The distance function is
The speed is the rate of change of the distance with respect to time.
This implies that the function for speed can be computed by differentiating the function for distance with respect to time.
Differentiate the function with respect to t to obtain:
To calculate: The interval at which the particle moves in the positive direction if .
To calculate: The interval where the particle is moving in the negative direction if .
To calculate: The time when the direction of the particle changes if .
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