Question

Suppose the dots below were made by an object moving left to right across the page. The interval of time between the formation of any two adjacent dots is the same. The numbers have no physical significance, they are just for reference to the intervals between dots:

      1              2                        3                              4                         5                6               

●          ●                    ●                              ●                              ●                    ●            ●

1. Draw and label a displacement vector for the object.

2. Draw appropriate velocity vectors for each interval between dots (you will need to draw and label 6 velocity vectors. Be sure to label each using the appropriate number for that interval and make the lengths the right proportions to each other.

3. Use graphical vector subtraction to generate and label a Δv vector for each pair of adjacent velocity vectors (there will be five). Label the vectors involved in the subtraction and the Δv vector in each case.

d. Draw & label an acceleration vector appropriate for each Δv vector.

Answer 1

First of all assume a time interval which is is same for all the consecutive  points. I have shown in the figure how the displacements are drawn. This is the most trivial of all.

The Displacement is marked as D_i where i =1,2,3,4,5,6

Velocity is marked as V_i

is marked as difference of two velocities shown by   where i=j+1 and j=1,2,3,4,5

acceleration is marked as a_{ij where} i=j+1 and j=1,2,3,4,5