Page 18 - 4167

1. A material point moves on an arbitrary curve. For

time t velocity of point changes from v to


v   v from the first to the second position .

2. To define acceleration it is necessary to
determine the change of velocity - vector
difference of velocity. For this purpose it is
necessary to do parallel transference of vector
2  
v   v

3. After parallel transference of vector, difference

 v includes change of velocity by direction and
magnitude .
3

4. To determine the change of velocity only by
magnitude we lay off along the second vector the
value of the first vector (its length). As a result we

get the vector v which determines the change
1
4
of velocity by magnitude .

5. If magnitudes of the first and the second

vectors are equal , the vector v determines
2
the change of velocity only by direction

5

Figure 1.9

As follows from fig 1.9 the complete vector change is vector sum
  
v   v   v 2 . (1.25)
1
So , average acceleration is equal to

17