a bus travels from one point to another wuth a speed of 40km/h and returns with a speed of 60km/h.what is e average speed and average velocity of the bus?
since the total displacement vector is zero the average speed is zero.
let i be unit vector from point A to point B
velocity outbound = 40 i
velocity back = -60 i
(40 - 60)/2 = -10
The average velocity is zero, but the speed is not.
The total distance covered is 2d. The total time taken is
d/40 + d/60 = 5d/120
So, the average speed is 2d/(5d/120) = 48 km/hr
Whoops, sorry, Steve is right.
To find the average speed of the bus, we need to consider the total distance traveled divided by the total time taken.
Let's assume the distance between the two points is "d."
When the bus travels from one point to another, it covers a distance of "d" at a speed of 40 km/h. The time taken for this journey would be "time1 = distance/speed" = "d/40."
When the bus returns from the second point to the initial point, it covers the same distance "d" at a speed of 60 km/h. The time taken for this journey would be "time2 = distance/speed" = "d/60."
The total time taken is the sum of time1 and time2: "total time = d/40 + d/60."
The average speed is then calculated by dividing the total distance covered (2d, as it covers the distance twice) by the total time taken (d/40 + d/60): "average speed = total distance / total time" = "2d / (d/40 + d/60)."
Simplifying the above expression, we get:
"average speed = 2d / (3d/120 + 2d/120)" = "2d / (5d/120)" = "2d * 120 / 5d" = "240 / 5" = 48 km/h.
Therefore, the average speed of the bus is 48 km/h.
Now let's calculate the average velocity. Velocity is a vector quantity, meaning it depends on both the magnitude and direction of motion.
Since the bus travels from one point to another and then returns to the starting point, its displacement is zero because displacement measures the change in position. Thus, the average velocity of the bus is zero.
To summarize:
Average speed of the bus = 48 km/h
Average velocity of the bus = 0 km/h (since it has zero displacement)