At 2:15 pm a passenger looks over at the speedometer and notices that they are going 55 miles per hour DUE WEST. at 2:37 pm this very passenger hears a siren and looks over the speedometer again; she notices that they are going 83 mph, DUE WEST. What was the magnitude of the average acceleration of the car at the time of the interval?
To determine the magnitude of the average acceleration of the car during the given time interval, we need to calculate the change in velocity over the given time.
Step 1: Calculate the change in velocity.
Change in velocity = Final velocity - Initial velocity
The initial velocity at 2:15 pm was 55 mph due west, and the final velocity at 2:37 pm was 83 mph due west.
Change in velocity = 83 mph - 55 mph
Change in velocity = 28 mph due west
Step 2: Calculate the time interval.
The time interval between 2:15 pm and 2:37 pm is 22 minutes.
22 minutes can be converted to hours by dividing by 60 (since there are 60 minutes in an hour).
Time interval = 22 minutes / 60
Time interval = 0.367 hours
Step 3: Calculate the average acceleration.
Average acceleration = Change in velocity / Time interval
Average acceleration = 28 mph due west / 0.367 hours
Average acceleration = 76.30 mph/hour due west
Therefore, the magnitude of the average acceleration of the car during the given time interval is 76.30 mph/hour.