Average velocity for the complete motion of the vehicle in ms-1

Question

a motor vehicle moves half of it's path with a velocity 60ms-1 and the other half with a velocity 40ms-1. Average velocity for the complete motion of the vehicle in ms-1

Answer 1

Average velocity = total distance/total time 

 

Begin by choosing a total distance covered, like 100 m (any distance will work, I'm just picking something easy)

 

Half of the total distance is 50 m

 

Calculate the time needed to travel 50 m at each velocity:

 

50m/60 ms^-1= 0.8333 s

 

and

 

50m/40 ms^-1 = 1.25 s

 

The total time to travel 100 m is 1.25 s + 0.8333 s = 2.083 s

 

Total distance was defined as 100 m, so

 

average velocity = 100 m travelled/2.083 s = 48 ms^-1 

 

 

Notice that the average is LESS than 50 ms^-1 (possibly the answer you expected).  This is because the vehicle spends MORE TIME (1.25 s versus 0.833 s) going SLOWER (40 ms^-1 versus 60 ms^-1) to cover the same distance (50 m).

 

 

Answer 2

Let d = the length of the vehicle's path.  The vehicle does d/2 at 60 m/s and the other d/2 at 40 m/s.  The total time it takes to cover the total distance d is:

 

d = rate × time, so time = d/rate:

 

time = (d/2)/60 + (d/2)/40

time = d/120 + d/80

time = 2d/240 + 3d/240 = 5d/240

 

The average speed of the vehicle is:

 

v = d/time = d/(5d/240) = ____ m/s