An object moves back anf forth along a straight line, with distance, s, in inches from its starting point, given by the equation.
$\displaystyle s=10^{2}-50t$

a) How far is it from its starting point after 4 seconds?
Why do I get -40?

b) How long will it take before it returns to its starting point?

Thank you!

2. Originally Posted by Coach
An object moves back anf forth along a straight line, with distance, s, in inches from its starting point, given by the equation.
$\displaystyle s=10t^{2}-50t$
I presume I have corrected the equation correctly?

Originally Posted by Coach
a) How far is it from its starting point after 4 seconds?
Why do I get -40?
The distance is given by s, so
$\displaystyle s(4) = 10\cdot 4^2 - 50 \cdot 4 = 160 - 200 = -40$
so you were right. BUT you are looking for the distance from the starting point, so your answer is 40. (The negative sign means that, if you are plotting this on a number line, the object's position is on the left of the origin.

Originally Posted by Coach
b) How long will it take before it returns to its starting point?
We want a t for s = 0. Thus
$\displaystyle 0 = 10t^2 - 50t$

$\displaystyle 0 = (10t)(t - 5)$

So either
$\displaystyle 10t = 0 \implies t = 0$
or
$\displaystyle t - 5 = 0 \implies t = 5$

The t = 0 solution is obviously true, since this is the starting point. So we are looking for the t = 5.

-Dan