How long did it take the driver to stop the car?

Question

A car is traveling at 26 meters per second (m/s) and accelerating at -13 m/s^2. After traveling 26 m, the driver brings the car to a complete stop. The equation is 26 = 26t - t^2, where t is the time it takes to stop, can be used to represent this situation.

Answer 1

That's not the correct equation to model this situation.  The correct equation is:

 

26 = 26t - (1/2)(-13)t²

 

Multiply both sides by (-2/13):

 

-4 = t² - 4t

0 = t² - 4t + 4

0 = (t-2)²

t = 2 seconds

 

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An even simpler equation to model the situation is v(t) = at + v₀, where:

• v(t) = speed at time t = 0 (when the car comes to s stop)
• a = acceleration = -13 m/s²
• v₀ = initial velocity = 26 m/s

 

v(t) = at + v₀

0 = (-13)t + 26

13t = 26

t = 2 seconds