Question

a car's velocity is modeled by
$v(t) = 0.5t {}^{2} - 10.5t + 45 \: for\leqslant t \leqslant 10.5$
Where velocity is in feet per second and time is in seconds. When does the car come to a complete stop?​

Answer 1

In accordance with the function velocity, the car will have a complete stop after 6 seconds.

When does the car stop?

Herein we have a function of the velocity of a car (v), in feet per second, in terms of time (t), in seconds. The car stops for t > 0 and v = 0, then we have the following expression:

0.5 · t² - 10.5 · t + 45 = 0

t² - 21 · t + 90 = 0

By the quadratic formula we get the following two roots: t₁ = 15, t₂ = 6. The stopping time is the least root of the quadratic equation, that is, the car will have a complete stop after 6 seconds.

To learn more on quadratic equations: https://brainly.com/question/2263981

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