When Does the Turtle Reach 10 cm from the Starting Point for the Third Time?

[physstudent1]

Homework Statement

A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t)=50.0cm+(2.00cm/s)\,t-(0.0625cm/s^2)t^2

At what time t is the turtle third time a distance of 10.0 {\rm cm} from its starting point?

Homework Equations

The Attempt at a Solution

Ok the first question asked for the first time, the second question was the second time, now it wants a third time, however its a parabola I don't see how it could have a third time.

I got .5(-.125)t^2+2t-10 for my equation did the quadratic equation and got 6.20seconds and 25.8 seconds. How can it possibly have a third time...? I don't know how to enter no solution into the program where we send our homework in we use Mastering Physics.

 

[PhanthomJay]

Homework Statement

A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is x(t)=50.0cm+(2.00cm/s)\,t-(0.0625cm/s^2)t^2

At what time t is the turtle third time a distance of 10.0 {\rm cm} from its starting point?

Homework Equations

The Attempt at a Solution

Ok the first question asked for the first time, the second question was the second time, now it wants a third time, however its a parabola I don't see how it could have a third time.

I got .5(-.125)t^2+2t-10 for my equation did the quadratic equation and got 6.20seconds and 25.8 seconds. How can it possibly have a third time...? I don't know how to enter no solution into the program where we send our homework in we use Mastering Physics.

The turtle starts off at 50 cm from the origin, and you have calculated its time when it reached 60 cm, two times. Which way is the turtle going the 2nd time? Where will it be as measured from the origin the third time it is 10cm away from its start point? The wording is a bit tricky, but it should jump out at you when you think about it a bit.

 

[physstudent1]

oh i think i got it so it goes hits 60 keeps going turns aroudn come back hits 60 again then keeps going and hits 40cm from orgin or 10 cm from starting position?

 

[PhanthomJay]

oh i think i got it so it goes hits 60 keeps going turns aroudn come back hits 60 again then keeps going and hits 40cm from orgin or 10 cm from starting position?

Yes! (except it doesn't actually turn around, it starts moving backwards at some point.)