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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 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

**of t=0 ---> t=2**

for part d

for part d

y(0) = 3

y(1) = 3.2

t(2) 3.8

distance = (3.8 - 3) = 0.8