How long will the car skid?

The function d(t) = 17t² - 110t gives the distance a car going a certain speed will skid in t seconds.  Find the time it would take for the car to skid 180 feet.

---

d(t) is the distance the car skids
t is the time the car skids

So, substitute 180 in for d(t), and then solve for t, to find the time the car skids for 180 feet.

180 = 17t² - 110t  {substituted 180 in for d(t)}
17t² - 110t - 180 = 0  {subtracted 180 from each side}

You can solve this equation by graphing it on the graphing calculator.  You are looking to see where the graph
intersects the x-axis (or in this case the t-axis).  That is the value of x (or t) that makes the y-value (or d(t))
equal to zero.  Also, you are only looking for the positive x-intercept, since time cannot be negative.

​

As you can see from the graph to the right, the
x-intercepts are -1.3 and 7.8.  Again, you are only looking for the positive x-intercept, which is 7.8.

Therefore, t, (how long the car will skid for 180 feet
is 7.8 seconds.

Ask Algebra House