A motorist drive 360 km from one city to another in 4.2 hours but makes the return trip in only 3 hours.What are the average speed and average velocity at each half? what is the total speed and velocity at m/s.
speed = distance/time
apply to your 3 cases.
Average speed = Total distance covered/total time taken.Now avg speed in going from one city to other=360/4.2=85.71 Km\h.
Similarly avg speed in returning the trip =360/3=120Km/h
Average velocity=Displacement/time taken
Avg velocity in going from one city to other = 360-0/4.2=85.71km/h
Similarly avg velocity in returning the trip =360/3=120km/h
Total speed=720/7.2=100km/h
In m\s it = 100x5/18=27.77m/s
Total velocity=27.77m/s
To find the average speed, we divide the total distance traveled by the total time taken.
For the first half of the journey (from city A to city B):
Distance = 360 km
Time = 4.2 hours
Average speed = Distance / Time
Average speed = 360 km / 4.2 hours
Average speed = 85.71 km/h
For the second half of the journey (from city B back to city A):
Distance = 360 km
Time = 3 hours
Average speed = Distance / Time
Average speed = 360 km / 3 hours
Average speed = 120 km/h
The average velocity is similar to average speed but takes into account the direction. Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. The direction from city A to city B is positive, while the direction from city B back to city A is negative.
The average velocity at each half can be calculated as:
Average velocity = (Change in displacement) / Time
For the first half (from city A to city B):
Displacement = Distance = 360 km (since the direction is positive)
Time = 4.2 hours
Average velocity = 360 km / 4.2 hours
Average velocity = 85.71 km/h (in the positive direction)
For the second half (from city B back to city A):
Displacement = -360 km (since the direction is negative)
Time = 3 hours
Average velocity = -360 km / 3 hours
Average velocity = -120 km/h (in the negative direction)
To find the total speed, we find the average of the average speeds:
Total speed = (85.71 km/h + 120 km/h) / 2
Total speed = 102.86 km/h
To find the total velocity, we consider the total displacement, which is zero:
Total velocity = Displacement / Time
Displacement = 0 km
Time = 7.2 hours (4.2 hours + 3 hours)
Total velocity = 0 km / 7.2 hours
Total velocity = 0 km/h
Therefore, the total speed is 102.86 km/h and the total velocity is 0 km/h.