A bus travels 80 km due south in 2 hours it then travels 100 km due west in 3 hours what is the average velocity of the bus
Well, I can give you average
in 5 hours goes 80 km S and 100 km west
average east (x component ) = -20 km/h
average north(y component) = -16 km/h
average speed = magnitude of velocity = sqrt(400+ 256)= 25.6 km/h
What is the difference between radial and tangential acceleration?
Well, it seems like this bus is having a bit of an existential crisis, going in different directions and all. But let's calculate its average velocity anyway!
To find the average velocity, we need to determine the total displacement and divide it by the total time taken.
The displacement in the south direction is 80 km and it took 2 hours, so the velocity in the south direction is 80 km/2 hours = 40 km/h.
The displacement in the west direction is 100 km and it took 3 hours, so the velocity in the west direction is 100 km/3 hours ≈ 33.33 km/h.
Now, we need to combine these two velocities using the Pythagorean theorem because they're in perpendicular directions.
The total displacement is the square root of (40 km/h)^2 + (33.33 km/h)^2.
Calculating this gives us a total displacement of approximately 51.96 km/h.
Therefore, the average velocity of the bus is approximately 51.96 km/h, because it's the magnitude of the resultant velocity vector.
Just remember, the bus may be a bit confused about its direction, but at least it's taking the scenic route!
To find the average velocity of the bus, we need to calculate the total displacement and total time traveled.
First, let's break down the given information:
- The bus travels 80 km due south in 2 hours.
- The bus then travels 100 km due west in 3 hours.
For the southward journey:
Distance = 80 km
Time = 2 hours
For the westward journey:
Distance = 100 km
Time = 3 hours
To calculate the total displacement, we need to find the resultant vector of both the southward and westward journey. This can be calculated using the Pythagorean theorem, as the displacement forms a right triangle:
Displacement = √(Distance south^2 + Distance west^2)
Displacement = √(80^2 + 100^2)
Displacement = √(6400 + 10000)
Displacement = √(16400)
Displacement ≈ 128.06 km
To calculate the total time traveled, we add the time for both the southward and westward journey:
Total Time = Time south + Time west
Total Time = 2 hours + 3 hours
Total Time = 5 hours
Average velocity = Total displacement / Total Time
Average velocity = 128.06 km / 5 hours
Average velocity ≈ 25.61 km/h
Therefore, the average velocity of the bus is approximately 25.61 km/h.
To find the average velocity of the bus, we need to calculate the total displacement and divide it by the total time elapsed.
The displacement is a vector quantity that indicates the change in position. In this case, the bus travels 80 km due south and 100 km due west. To calculate the total displacement, we can use vector addition.
Let's break down the displacements into their horizontal (east-west) and vertical (north-south) components:
- The displacement due south has a magnitude of 80 km and points in the negative y-direction.
- The displacement due west has a magnitude of 100 km and points in the negative x-direction.
Let's represent the horizontal component as Dx and the vertical component as Dy.
Dx = -100 km
Dy = -80 km
To calculate the total displacement using vector addition, we can use the Pythagorean theorem:
Displacement (D) = sqrt(Dx^2 + Dy^2)
D = sqrt((-100 km)^2 + (-80 km)^2)
D = sqrt(10000 km^2 + 6400 km^2)
D = sqrt(16400 km^2)
D ≈ 128.06 km
Now that we have the total displacement, we need to calculate the total time elapsed:
Total time elapsed = 2 hours + 3 hours
Total time elapsed = 5 hours
Finally, we can calculate the average velocity by dividing the total displacement by the total time elapsed:
Average velocity = Total displacement / Total time elapsed
Average velocity = 128.06 km / 5 hours
Average velocity ≈ 25.61 km/h
Therefore, the average velocity of the bus is approximately 25.61 km/h.