A few problems regarding motion

[I R GOOD]

1. The problem statement, all variables and given/known data

2.15

A turtle crawls a straight line, which we call the x-axis with positive direction to the right.Equation for the turtle's position as a function of time

is x(t)=50,0cm + (2,0cm/s)t - (0,625cm/s^2)t^2


a.) find the turtle's initial velocity, initial position, initial acceleration

b.) at what time t is the velocity of the turtle zero (derivation?)

c.) how long after does it take the turtle to return to it's starting point

d.)At what time t is the turtle a distance of 10,0cm from it's starting poin



3. The attempt at a solution

a.) Initial position at x(0)
50cm +(2cm/s)(0) -(0,065cm/s)(0)
=50cm

Initial velocity
x'(0) =0 + (2cm/s)(1) -(0,065cm/s^2)(2*0)
=2cm/s

initial acceleration
x''(0) = 0 + (-0,065cm/s^2)(2)
= -0,125cm/s^2

b.)
at what time t is the velocity of the turtle zero
x'(t)= 0 + (2cm/s)(1) - (0,065cm/s^2)(2t)

then x'(t) = 0

2cm/s - (0,0625cm/s^2)(2t) = 0
1cm/s =(0,0625cm/s^2)(t)
1cm/s / -0,0625cm/s^2=t
= -16s


c.) how long after does it take the turtle to return to it's starting point

I tried

(-0,065cm/s^2)(t^2) + (2cm/s)(t) + 50cm = 0

QUADRATIC FORMULA

got either -16,49..... or 48,3...
but answer should be 32s


same with d.)

[LowlyPion]

Welcome to PF.

Maybe there was a typo in the problem?

Maybe it should have been .0625 and not .065 in the statement?

[I R GOOD]

Hello and thank you.

I double checked, and yes it was indeed a typo. No wonder... :)

[I R GOOD]

a.) and b.) are now correct, but am I doing something wrong in c?

[LowlyPion]

The starting point is at 50 cm.