Final answer:
To calculate the distance a car traveling at 20 mi/s stops in 4 seconds, we use kinematic equations. The car decelerates uniformly, and the calculated distance is 40 miles.
Step-by-step explanation:
The question asks to calculate the distance traveled by a car which is decelerating to a stop from an initial speed. To solve this, we can use the kinematic equations for uniformly accelerated motion, which includes deceleration in this context.
Given that the car's initial velocity is 20 miles per second (which is an unusually high speed and likely a typo, but we'll use it as given for this exercise), and it comes to a stop in 4 seconds, we can assume uniform deceleration. The kinematic equation we can use is:
d = v_i * t + (1/2) * a * t^2
Here, d is the distance traveled, v_i is the initial velocity, t is the time and a is the acceleration (which will be negative in the case of deceleration).
Because the final velocity v_f is 0 (the car stops), we can also use the equation v_f = v_i + a * t to find the acceleration. Rearranging to solve for a, we get a = (v_f - v_i) / t which simplifies to a = -v_i / t. Plugging the values in, we find the deceleration is -5 mi/s^2.
Substituting v_i = 20 mi/s, t = 4 s, and a = -5 mi/s^2 into the distance equation, we get:
d = (20 mi/s * 4 s) + (1/2) * (-5 mi/s^2) * (4 s)^2
This simplifies to:
d = 80 mi - 40 mi
d = 40 miles
Therefore, the car travels a distance of 40 miles before coming to a stop.