Question

Derive the formula... v= u + at

Answer 1

Consider the velocity – time gra.Velocity–Time graph to derive the equations of motion.The body has an initial velocity u at point A and then its velocity changes at a uniform rate from A to B in time t. In other words, there is a uniform acceleration 'a' from A to B, and after time t its final velocity becomes 'v' which is equal to BC in the graph. The time t is represented by OC. To complete the figure, we draw the perpendicular CB from point C, and draw AD parallel to OC. BE is the perpendicular from point Bto OE.Now, Initial velocity of the body, u=OA...... (1)And, Final velocity of the body, v=BC........ (2)But from the graph BC=BD + DCTherefore, v=BD + DC ......... (3)Again DC=OASo, v=BD + OANow, From equation (1), OA=uSo, v=BD + u ........... (4)We should find out the value of BD now. We know that the slope of a velocity – time graph is equal to acceleration, a.Thus, Acceleration, a=slope of line ABor a=BD/ADBut AD=OC = t,so putting t in place of AD in the above relation, we get:a=BD/tor BD=atNow, putting this value of BD in equation (4) we get :v=at + uThis equation can be rearranged to give:v=u + atAnd this is the first equation of motion. It has been derived here by the graphical method.

Answer 2

We know
that
v-u
a=-------------
t
v-u=at

v=u+at