Question

The position of a particle moving on the x-axis at time t>0 seconds is: x(t)= e^t - t^1/2.

a) Find the average velocity of the particel over the interval [1,3].

b) In what direction and how fast is the particle moving at t= 1 seconds?

c) For what values of t is the particle moving to the right?

d) Find the postition of the particle when its velocity is 0.

Answer 1

a) Calculate the change in x from t=1 to t=3 and divide by 2 s for athe anverage velcoity

b) Calculate dx/dt at t=1
velocity = dx/dt = e^t - (1/2)/t^1/2

c) Find out when dx/dt > 0 . That will be the answer. You may need to graph dx/dt

d) Solve for t when dx/dt = 0
Use that t in the x(t) equation.

These are exercises you should be able to do yourself. Someone will gladly critique your work.