Final answer:
To find the acceleration of the car, we can use the equation a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken. The acceleration is equal to 1.93651 miles per square hour.
Step-by-step explanation:
To find the acceleration of a car, we can use the equation a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken.
In this case, the car stops, so the final velocity is 0 mph. The initial velocity is given as 74 mph. We need to convert these velocities to feet per second to match the units of the distance. 1 mile is approximately equal to 5280 feet, and 1 hour is equal to 3600 seconds. Therefore, 74 mph is equal to (74 * 5280) / 3600 = 108.8 feet per second.
The distance traveled by the car is given as 197 feet.
Now we can use the formula a = (v_f - v_i) / t. Rearranging the formula, we get t = (v_f - v_i) / a. Plugging in the values, t = (0 - 108.8) / a = -108.8 / a. We know that the time cannot be negative, so the magnitude of acceleration must be positive. Therefore, we take the absolute value of the acceleration.
Using t = -108.8 / a and the distance traveled, we can also use the equation d = v_i * t + 0.5 * a * t^2 to find the acceleration. Rearranging the formula, we get a = (d - v_i * t) / (0.5 * t^2). Plugging in the values, a = (197 - 108.8 * t) / (0.5 * t^2).
The acceleration is measured in feet per second squared. To convert it to miles per square hours, we need to convert feet to miles and seconds to hours. 1 foot is equal to 0.000189394 miles, and 1 second is equal to 0.000277778 hours. Therefore, 1 foot per second squared is equal to (0.000189394 * 3600) / 0.000277778 = 1.93651 miles per square hour.