I don't get the same results in a Pytel dynamics problem

[Alexanddros81]

Hi!
I have Pytel Mechanics Dynamics 2nd edition and revising for my own purposes (not a homework).
I am trying to solve problem 12.4:

A bead moves along a straight 1500-mm wire that lies along the x-axis. The position of the bead
is given by
x=t² - 10t mm
where x is measured from the center of the wire, and t is the time in seconds. Determine
a) the time when the bead leaves the wire; and b) the distance traveled by the bead from t=0 until
it leaves the wire

I get (a) to be 32.83sec which is correct according to even-numbered answers given at the back of the
book but (b) is given to be 2000mm which is not what I get. I get 800mm

Can you verify if my answer to (b) is correct or tell me what is your answer of (b)?

Does anyone has all the answers of the book I mentioned?

thanks

 

[BvU]

I get 800 too: t² - 10t = (t-5)² - 25 , so it evaluates to -25 mm at t=5 .

I don't have all the answers

 

[Alexanddros81]

After trying to calculate (b) analytically and failed to get 2000mm
today I differentiated x to get the velocity which is 2t-10. I plotted the graph
and calculated the area of the two triangles. that gave me aproximately 800mm
I used https://www.desmos.com/calculator to do the plot.

 

[BvU]

After trying to calculate (b) analytically

It goes 25 mm to the left and then 775 to the right. 800 mm of travel.
Don't waste much more time on this and move on to the next !

 

[vanhees71]

Also note that this book is very sloppy concerning dimensions. The correct formula must read
$$x(t)=\frac{a}{2} t^2 +v t,$$
where $a$ is the constant acceleration and $v$ the initial velocity. In other words the constants in front of $t$ must have the correct dimensions to be a valid formula in physics.