a = 3.09 m/s²
Explanation
This question doesn't tell anything about how long it took for the car to go through 105 meters. As a result, the timeless suvat equation is likely what you need for this question.
In the timeless suvat equation,
[tex]a = \dfrac{v^2 - u^2}{2\; x}[/tex]
where
- [tex]a[/tex] is the acceleration of the car;
- [tex]v[/tex] is the final velocity of the car;
- [tex]u[/tex] is the initial velocity of the car; and
- [tex]x[/tex] is the displacement of the car.
Note that v and u are velocities. Make sure that you include their signs in the calculation.
In this question,
- [tex]a[/tex] is the unknown;
- [tex]v = -10.9 \; \text{m} \cdot \text{s}^{-2}[/tex];
- [tex]u = -27.7 \; \text{m} \cdot \text{s}^{-2}[/tex]; and
- [tex]x = - 105 \; \text{m}[/tex].
Apply the timeless suvat equation:
[tex]a = \dfrac{v^{2} - u^{2}}{2\; x}\\\phantom{a} = \dfrac{(-10.9)^{2} - (-27.7)^{2}}{2 \times (-105)}\\\phantom{a} = 3.09 \; \text{m} \cdot \text{s}^{-2}[/tex].
The value of [tex]a[/tex] is greater than zero, which is reasonable. Velocity of the car is negative, meaning that the car is moving backward. The car now moves to the back at a slower speed. Effectively it accelerates to the front. Its acceleration shall thus be positive.
