Final answer:
To calculate the stopping distance of a car decelerating at 4 m/s^2 from 40 m/s, the equation v^2 = u^2 + 2as is used, resulting in a stopping distance of 200 meters.
Step-by-step explanation:
A woman driving a car traveling at 40 m/s slams on the brakes and decelerates at 4 m/s2. To calculate how far the car will travel before it stops, we can use the formula for displacement under constant acceleration, which is:
v2 = u2 + 2as,
where v is the final velocity, u is the initial velocity, a is the acceleration (deceleration in this case since it will be negative), and s is the displacement.
Since the car comes to a stop, v = 0 m/s, so the formula becomes:
0 = (40 m/s)2 + 2(-4 m/s2)s,
0 = 1600 m2/s2 - 8s,
s = 1600/8 = 200 meters.
Therefore, the car travels 200 meters before it comes to a stop.