Final answer:
Using kinematic equations, we find the car's deceleration to be -9 m/s^2, and calculate the time to stop to be approximately 3.33 seconds.
Step-by-step explanation:
When a car moving at 30m/s comes to rest over a distance of 50m when the brakes are applied, we can use the kinematic equations to determine the time it takes to stop. The equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, can be rearranged to find the acceleration (a).
We know that the car comes to rest, so v = 0 m/s, u = 30 m/s, and s = 50 m. Substituting these values gives us 0 = (30 m/s)^2 + 2 * a * 50 m. Solving for a, we get a = -(30 m/s)^2 / (2 * 50 m), which simplifies to a = -9 m/s^2. Now, using the equation v = u + at, and solving for t, we have 0 = 30 m/s + (-9 m/s^2) * t, which gives us t = 30 m/s / 9 m/s^2 or approximately 3.33 seconds to stop.