A motorcycle officer hidden at an intersection observes a car driven by an oblivious driver who ignores a stop sign and continues through the intersection at constant speed. The police officer takes off in pursuit 1.98 s after the car has passed the stop sign. She accelerates at 3.9 m/s2 until her speed is 114 km/h, and then continues at this speed until she catches the car. At that instant, the car is 1.7 km from the intesection.
(a) How long did it take for the officer to catch up to the car?
59.72 s
(b) How fast was the car traveling?
mi/h
20.976s... trust me...
In order to convert the car's speed from meters per second to miles per hour, we need to use the conversion factor. 1 meter per second is equivalent to approximately 2.237 miles per hour.
First, let's calculate the car's speed in meters per second. The car traveled a distance of 1.7 km from the intersection, which is equivalent to 1700 meters. The car took 1.98 seconds to reach that distance. Using the formula speed = distance / time, we can calculate the car's speed:
Car's speed = 1700 meters / 1.98 seconds
Car's speed ≈ 858.5869 meters per second
Now, let's convert this speed to miles per hour:
Car's speed ≈ 858.5869 meters per second * 2.237 miles per hour
Car's speed ≈ 1923.9725 miles per hour
Therefore, the car was traveling at approximately 1924 miles per hour.