# AP Calculus

## 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 dont 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

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The part letter b asks only for a direction, so the answer should either be positive or negative. In part letter d, you would do better to identify the roots of the displacement equation and find the displacements in each direction (the intervals separated by the zeroes), and then add the absolute value of the results up. This is because the particle is travelling in one dimension and the question asks for distance and not displacement.

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The part letter b asks only for a direction, so the answer should either be positive or negative. In part letter d, you would do better to identify the roots of the displacement equation and find the displacements in each direction (the intervals separated by the zeroes), and then add the absolute value of the results up. This is because the particle is travelling in one dimension and the question asks for distance and not displacement.
so for d can I use the distance formula?