Assuming the driver starts slamming the brakes immediately, the car moves by uniformly decelerated motion, so we can use the following relationship
[tex]2aS = v_f^2 - v_i^2[/tex] (1)
where
a is the deleceration
S is the distance covered after a time t
[tex]v_f[/tex] is the velocity at time t
[tex]v_i=100 km/h = 27.8 m/s[/tex] is the initial speed of the car
The accident is 80 m ahead of the car, so the minimum deceleration required to avoid the accident is the value of a such that S=80 m and [tex]v_f=0[/tex] (the car should stop exactly at S=80 m to avoid the accident). Using these data, we can solve the equation (1) to find a:
[tex]a=- \frac{v_i^2}{2 S}= -\frac{(27.8 m/s)^2}{2 \cdot 80 m} =-4.83 m/s^2 [/tex]
And the negative sign means it is a deceleration.
