A motorist drives north at 28m/s for 5 minutes, turns around and then drives 25m/s in the opposite direction for 3 minutes calculate the average speed and the average velocity for the whole journey
avg speed = distance/time = (28*5 + 25*3)/(5 + 3) = 26.875 m/s
avg velocity = (28*5 - 25*3)/(5+3) = 8.125 m/s
where the + value indicates a net north velocity
Yes, I know that 5 minutes is 5*60=200 seconds, but since the factor of 60 occurs both in the top and bottom, it cancels out. As written, the units are (m/s*min)/(min), which equates to m/s.
To calculate the average speed, we need to find the total distance traveled and divide it by the total time taken.
1. Distance traveled in the first leg (north):
Speed = 28 m/s
Time = 5 minutes = 5 * 60 seconds = 300 seconds
Distance = Speed * Time = 28 m/s * 300 seconds = 8,400 meters
2. Distance traveled in the second leg (opposite direction):
Speed = 25 m/s
Time = 3 minutes = 3 * 60 seconds = 180 seconds
Distance = Speed * Time = 25 m/s * 180 seconds = 4,500 meters
3. Total distance traveled:
Distance = Distance of first leg + Distance of second leg
Distance = 8,400 meters + 4,500 meters = 12,900 meters
4. Total time taken:
Time = Time of first leg + Time of second leg
Time = 300 seconds + 180 seconds = 480 seconds
Average speed = Total distance traveled / Total time taken
Average speed = 12,900 meters / 480 seconds = 26.875 m/s (rounded to three decimal places)
Now, let's calculate the average velocity. Velocity is a vector quantity, which means it has both magnitude and direction. The magnitude of the average velocity will be the average speed, and the direction will be the same as the initial direction (north).
Average velocity = Average speed = 26.875 m/s (rounded to three decimal places)
To calculate the average speed and average velocity for the whole journey, we need to first determine the total distance traveled and the total displacement.
1. Calculate the distance traveled in the first leg of the journey:
Distance = Speed × Time
Distance = 28 m/s × (5 minutes × 60 seconds/minute) = 28 m/s × 300 s = 8400 meters
2. Calculate the distance traveled in the second leg of the journey:
Distance = Speed × Time
Distance = 25 m/s × (3 minutes × 60 seconds/minute) = 25 m/s × 180 s = 4500 meters
3. Calculate the total distance traveled:
Total Distance = Distance of First Leg + Distance of Second Leg
Total Distance = 8400 meters + 4500 meters = 12900 meters
4. Determine the displacement:
Displacement is the difference between the initial position and the final position. Since the motorist drives north and then turns around and drives in the opposite direction, the displacement is zero. This means the motorist ends up at the same position they started.
Now, we can calculate the average speed and average velocity:
Average Speed = Total Distance ÷ Total Time
Average Speed = 12900 meters ÷ ((5 minutes + 3 minutes) × 60 seconds/minute)
Average Speed = 12900 meters ÷ (8 × 60 seconds) = 26.875 m/s (rounded to three decimal places)
Average Velocity = Displacement ÷ Total Time
Average Velocity = 0 meters ÷ ((5 minutes + 3 minutes) × 60 seconds/minute)
Average Velocity = 0 meters ÷ (8 × 60 seconds) = 0 m/s
Therefore, the average speed for the whole journey is approximately 26.875 m/s, and the average velocity is 0 m/s.