- #1
gonzalo12345
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Homework Statement
A particle moves along the y-axis with position defined by y(t) = -1/2cos(t^2) + 7/2 t≥ 0
a. find(2)
b. in which direction is the particle moving at time t=1.5?
c. 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?
d. Find the total distance traveled by the particle from t=0 to t=2
Homework Equations
related rates, derivatives
The Attempt at a Solution
I tried to solve the problem but I don't know if its right in some parts, so can somebody help me to see if there is something wrong, thanks
for part a I got y(2) = 3.83
for part b v(t) = tsint^2
v(1.5) = 1.5sin(1.5^2)
= 1.167
for part c: a(t) = sin(t^2) + 2(t^2)cos(t^2)
a(1.5) = -2.04
No, because the acceleration and the velocity doesn't have the same sign
for part d of t=0 ---> t=2
y(0) = 3
y(1) = 3.2
t(2) 3.8
distance = (3.8 - 3) = 0.8