From Pillar to Post. Starting from a pillar, you run 200 m east (the +x-direction) at an average speed of 5.0 m>s, and then run 280 m west at an average speed of 4.0 m>s to a post. Calculate (a) your average speed from pillar to post and (b) your average velocity from pillar to post.
- you run 200 m east with average speed 5.0 m/s
so average speed = distance / time,
hence time = distance / average speed.
thus time = 200/5 = 40 seconds.
also now it’s position vector is 200 m (x).
- now you run 280 m west i.e. in -x direction since you specified east to be +x.
using the same expression of time as above , time = 280/4 = 70 seconds.
now your position vecor is 200 m (x) - 280m (x) = - 80m (x)
(a) your average speed for whole journey is total distance divided by total time = (200 + 280 )m/ (40 + 70 )seconds = 480m/110seconds = 4.36 m/s
(b) average velocity is total dispacement/ total time = final position - initial position/ total time = -80m (x) - 0 / 110 seconds = -80/110 m/s (x) = -0.727m/s (x) or you can say 0.727m/s in negative x or west direction.
Since average velocity is vector, it has got direction but average speed is scalar so it has no direction.