Kinematics

Average speed and average velocity

Average speed and average velocity take into account that the speed or velocity may not be constant over a given distance and is given by:

average speed = total distance travelled
                        total time taken

average velocity = total distance travelled in a particular direction
                           total time taken

Example 3: A man walks 500 m due east in 300 s and then a further 400 m in 320 s in the same direction. Determine his velocities for the 500 m, the 400 m and his average velocity for the whole journey.

For the 500 m:
v = 500/300 which gives 1.67 m/s due east

For the 400 m:
v = 400/320 which gives 1.25 m/s due east

Average velocity = 500 + 400
                           300 + 320

= 1.45 m/s due east

Note that in this case the average speed will also be 1.45 m/s due to the same direction travelled in each instance.

Example 4: A man walks 500 m due east in 300 s followed by 400 m due west in 320 s. Determine:

A) his average velocity for i) 500 m, ii) 400 m
B) his average velocity for the whole journey

Consider the direction east to be positive and the direction west to be negative. Therefore there will be no need to write the directions for distance and velocity as these will be shown as positive or negative numbers.

A) i) for 500 m: v = 500/300
v = 1.67 m/s

ii) for 400m: v = -400/320
v = -1.25 m/s

B) The actual distance travelled in a particular direction in 620 seconds (300+320) is 500 +(-400) = 100 m in an easterly direction.

Although the man has walked a total distance of 900 m, he has effectively only walked 100 m east because he changed direction in the lat 400 m.

Therefore the actual distance travelled in a particular direction is called a displacement.
And the average velocity of the man = 100/(300 + 320)
                                                     = 0.16 m/s

Note that the average speed of the man will be:
900/620 = 1.45 m/s as the man has still walked 900 m in 620 s.