Posted by Taeyeon on Sunday, February 26, 2012 at 2:45am.
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? Why?
b. Find the acceleration of the particle at time t= 1.5. Is the velocity of the particle increasing at t = 1.5? Why or why not?
c. Given that y (t) is the position of the particle at time t and that y (0) = 3, find y (2).
d. Find the total distance traveled by the particle from t = 0 to t = 2.

calculus  Reiny, Sunday, February 26, 2012 at 7:59am
v(t) = t sin t^2
a(t) = t( cos t^2) (2t) + sin t^2
= 2t^2 cos t^2 + sin t^2
y(t) = (1/2) (cos t^2) + c
given : when t = 0 , y(0) = 3
3 = (1/2)cos 0 + c
3 = 1/2 + c
c = 3.5
so y(t) = (1/2) cos t^2 + 3.5
You now have enough to answer all the other questions.
Remember that if the first derivative is posititive, the function is increasing, (if a(t) > 0, then v(t) increases)
y(2) = (1/2) cos (4) + 3.5 = appr 4.8
y(0) = 3
so the distance traveled from t0 to t2 = 4.83 = 1.8
Answer This Question
Related Questions
 Calculus  a particle starts at time t = 0 and moves along the x axis so that ...
 calculus  5. A particle moves along the xaxis in such a way that its position ...
 calculus  Consider a particle moving along the xaxis where x(t) is the ...
 Calculus (Answer Check)  A particle moves along the xaxis so that its velocity...
 Calculus (Answer Check)  A particle moves along the xaxis so that its ...
 Calculus AB  A particle is moving along the xaxis so that at time t its ...
 calculus  A Particle moves along the xaxis so that at any time t>0, its ...
 Calculous  A particle moves along the caxis so that at time t its position is ...
 Physics  A particle starts from the origin at t = 0 and moves along the ...
 math  a particle starts at time t = 0 and moves along the x  axis so that its ...
More Related Questions