The average speed is the distance covered divided by the time it took to cover this
If a person walks 1 km west, then turns around and walks 1 km east, the distance this
person covers is 2 km. If it takes 20 minutes to cover this distance then the average speed
is 2 km/ 20 minutes = 2000m/ (20*60s) = 1.67 m/s.
The average velocity is a vector. It is the displacement vector pointing from the initial
position to the final position, divided by the time. In the above example the initial and
the final position are the same. The displacement vector is zero. So the average velocity
In problem 3 on assignment 2 the person starts at point A and returns to point A. The
displacement vector is zero.
In problem 1, the length of the displacement vector is sqrt(152 +202). The time interval
is 10 s. The magnitude of the velocity vector is the length of the displacement vector
divided by the time interval.
In problem 4 we are asked to find the average speed for the whole trip. We do not know
the distance traveled, only the average speed for two sections of the trip.
In problems of this type you denote the unknown distance with some variable, for
example d, and hope that in the answer that variable cancels out.
The person walks a distance d from A to B with speed v1.
It takes a time t1 to cover the distance d.
t1 = d/v1
Now the person walks a distance d from B to A with speed v2.
It takes a time t2 to cover the distance d.
t2 = d/v2
The total distance covered is 2d.
The total time is t = t1 + t2 = d*(1/v1 + 1/v2)
The average speed is 2d/t.
The distance d cancels out.
The average acceleration is a vector. It is the velocity vector at the final time, minus the
velocity vector at the initial time, divided by the time interval.
In problem 2 choose your coordinate system so that vectors pointing east are denoted by
positive numbers and vectors pointing west are denoted by negative numbers.
Then the final velocity is vf = –2m/s.
The initial velocity is vi = 2m/s
The average acceleration is (vf – vi)/ delta t
If this is a negative number, it means it points to the west.
When an object turns, the velocity vector changes direction.