Problem 29.

(a) If a particle's position is given by   (where t is in seconds, and x is in meters), what is it's velocity at t=1s? 

(b) what is it's speed at t=1s? 

(c) Is there ever an instant when the velocity is 0?  If so, give the time.

Solution:

The velocity is the derivative of x(t) with respect to time. Then

(a) at t=1 s we get:

What we calculate here is an x-component of velocity. The negative sign means that the direction of velocity is opposite to the direction of axis x.

(b) the speed is the magnitude of velocity. Then at t=1 s the speed is 4 m/s

(c) to find time at which the velocity is 0 we just need to solve an equation:

From this equation we find time:

At this moment of time the velocity is 0.