Question

A car's velocity is modeled by V(t)=0.5t^2 -8t +24 ,where the velocity is in feet per second and time is in seconds. When does the car come to a complete stop

12 seconds
8 seconds
4 seconds
2 seconds

Answer 1

The car's velocity reaches zero and comes to a complete stop at 4 seconds as provided by the quadratic equation V(t) = 0.5t^2 - 8t + 24.

Step-by-step explanation:

To determine when a car comes to a complete stop, we need to find when its velocity is zero. The car's velocity is given by the quadratic equation V(t) = 0.5t^2 - 8t + 24. To find the time at which the velocity is zero, we have to solve the equation V(t) = 0.

Setting V(t) equal to zero, we obtain:

0 = 0.5t^2 - 8t + 24

Now, we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. However, the provided answers suggest that factoring might be the simplest approach. Let's see if the equation can be factored directly.

By checking the answer choices and plugging them into the equation, we find that at t = 4 seconds, the equation is true:

0 = 0.5(4)^2 - 8(4) + 24

0 = 0.5(16) - 32 + 24

0 = 8 - 32 + 24

0 = 32 - 32

0 = 0

Therefore, the car comes to a complete stop at 4 seconds.