AP Calculus
posted by some kid .
The position of a particle moving on the xaxis 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.

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.
Respond to this Question
Similar Questions

Calculus III
A particle is moving in R2 according to the law x=t^2, y=t^3 (time is measured in seconds, coordinates in meters). (a) What is the average velocity of the particle over the time interval [1,1.1]? 
physics
In this problem you will determine the average velocity of a moving object from the graph of its position as a function of time . A traveling object might move at different speeds and in different directions during an interval of time, … 
calculus
let f(t) = 2*pi*t + sin(2*pi*t) a) find value of t in open interval (0,2) for which the tangent line at (t, f(t)) is parallel to the line through (0,0( and (2, 4pi) b) suppose the given funtion describes the position of a particle … 
Calculus
At time t >or= to 0, the position of a particle moving along the xaxis is given by x(t)= (t^3/3)+2t+2. For what value of t in the interval [0,3] will the instantaneous velocity of the particle equal the average velocity of the … 
calculus
5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5? 
calculus
A particle is moving along the x axis so that its velocity at any time t ≥0 is give by v(t) = (2 pi  5)t  sin(pi t) A. Find the acceleration at ay time t. B. Find the minimum acceleration of the particle over the interval … 
Calculus
The displacement (in meters) of a particle moving in a straight line is given by s=2t^3 where is measured in seconds. Find the average velocity of the particle over the time interval [10,13]. the average velocity is 798 What is the … 
Calculus
The position of a particle moving on a horizontal line is given by s(t)=2t^315t^2+24t5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? 
calculus
A particle moves on a line so that its position at time t seconds is p(t)=3t3 meters to the right of the origin. Find the time c in the interval (4,8) for which the velocity of the particle at time c is equal to the average velocity … 
Calculus
Sorry this is really long. Just wondering how I would do each of these A particle is moving with velocity v(t) = t^2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between …