Answer:
it takes the car 4.362 seconds to cover the distance of 88.4 m.
Explanation:
The distance the car covers is given by the function
[tex]x(t) = vt-\dfrac{1}{2}at^2[/tex],
where [tex]v = 25.5m/s[/tex] , and [tex]a = 2.40m/s[/tex], putting these in we get:
[tex]x(t) = 25.5t-\dfrac{1}{2}(2.4)t^2\\\\x(t) = 25.5t-1.2t^2[/tex]
Now, when the car has moved to 88.4m, [tex]x(t) = 88.4[/tex] , or
[tex]x(t) = 25.5t-1.2t^2 = 88.4[/tex]
which is a quadratic equation with solutions
[tex]t = 4.362s,\\t = 16.887s[/tex]
We take the first solution [tex]t = 4.362s[/tex], since at that time the car is still moving right and decelerating. The second solution [tex]t =16.887[/tex] describes the situation where the car has stopped decelerating and is now moving leftwards because the decelerating is leftwards, which is utterly wrong because we know that cars do not start moving backwards after the brakes have stopped them!
Thus, it takes the car 4.362 seconds to cover the distance of 88.4 m.
