A hockey puck is hit on a frozen lake and starts moving with a speed of 9.7 m/s. 4.1 seconds later, its speed is 7.2 m/s.
(c) How far does the puck travel during the time interval?
To find the distance traveled by the puck during the time interval, we can use the average speed formula.
The average speed is defined as the total distance traveled divided by the total time taken.
We are given the initial speed and the final speed of the puck, as well as the time interval. From this information, we can calculate the average speed.
First, let's find the acceleration of the puck during the time interval. Acceleration is the rate at which speed changes, given by the formula:
Acceleration = (Final speed - Initial speed) / Time
Acceleration = (7.2 m/s - 9.7 m/s) / 4.1 s
Simplifying this expression, we get:
Acceleration = (-2.5 m/s) / 4.1 s = -0.61 m/s^2
Note that the negative sign indicates a decrease in speed.
Next, we can use the average speed formula to find the distance traveled by the puck. The average speed is given by the formula:
Average speed = (Initial speed + Final speed) / 2
Average speed = (9.7 m/s + 7.2 m/s) / 2
Average speed = 16.9 m/s / 2 = 8.45 m/s
Now, we can use the average speed and the time interval to find the distance traveled. The distance is equal to the average speed multiplied by the time interval:
Distance = Average speed * Time
Distance = 8.45 m/s * 4.1 s
Distance = 34.645 m
Therefore, the puck travels a distance of approximately 34.645 meters during the time interval.