Tracking a Particle's Motion Along the x-Axis

[hankjr]

A particle moves along the x-axis so that its velocity is given by
v(t)= -(t+1)sin(t^2/2)
****at time t=0, the particle is at position x=1

a) Find the acceleation of the particle at time t=2. Is the speed of the particle increasing at t=2? Why or Why not?

b) Find all times t in the open interval 0,t,3 when the particle changes direction.Justify your answer.

c)Find the total distance traveled by the particle from time t=0 until time t=3

d) During the time interval 0<=t<=3, , what is the greatest distance between the particle and the origin?

I WOULD GREATLY APPRECIATE IT IF SOMEONE WOULD HELP ME OUT ON THIS PROBLEM AND GIVE ME THE CORRECT ANSWERS SO I CAN SEE IF MINE ARE CORRECT. I'M DESPERATE , PLEASE HELP
- ALLEN

 

[stunner5000pt]

here are some hints but POST WHAT WORK YOU HAVE DONE (read the sticky at the top of the main page)

a) How is acceleration related to velocity? How do you find acceleration from velocity? Read your text, it probably gives you the clue or is answered in an example

b) When you change direction what is your velocity? Suppose you were running forward then what do you need to do to start running in the oppostie direction? You can't just turn around when you're at full stride! You will get multiple answers, use the ones that fall within the given interval.

c) how is distance related to velocity and time??
d = (average velocity) x time

d) write the distance between a point (t,v(t)) and the origin. How you maximize the distance? You will find many answers. USe the answer that falls withing the limits of the given interval.