Question

1) Prof that
v=utat
; 2 a 2 =2a8​

Answer 1

Answer:

v = u + at

Explanation:

Derivation of the Equation of motion for Velocity-time relation:-

1. First draw a v-t graph, taking time in x-axis and velocity in y-axis.
2. From the graph; it is observed that , initial velocity is 'u' at point "A" but here u not = 0.
3. The initial velocity 'u' increases to final velocity 'v' at point "B" in time 't'.
4. The velocity changes at uniform rate ,i.e. 'a'.
5. 2 perpendicular lines BC and BE are drawn from point 'B' on the time and velocity-axes respectively.
6. Hence, u = OA, v = BC and t = OC. So, BD = BC - CD where BD = change in velocity in time interval.
7. Let's draw AD parallel to OC. So, we see that :- BC = BD + CD

=> BC = BD + OA

8. Putting BC = v , OA = u , we have :-

=> v = BD + u

=> BD = v-u ------ (1)

9. From the v-t graph, acceleration of the object is given by :- a = change in velocity / time

= BD/AD OR BD/ OC

10. Putting OC = t, we get :-

=> a = BD/t

=> BD = at ------- (2)

Equating (1) and (2),

v - u = at

=> [v = u + at]

Therefore, the equation of motion for Velocity-time relation is derived by graphical method successfully.

Hence , proved . ✓