Derive the equation of motion v2 = u2 + 2ax using v-t graph
Answers
Answer:
u: velocity at time t1
v: velocity at time t2
a: uniform acceleration of the body along the straight line
Displacement covered during the time interval t2 - t1 = Area ABt1t2
S = Area of triangle ABA’ + Area of rectangle AA’t2t1 = Area of trapezium
S = ½ x Sum of parallel sides x Perpendicular distance
begin mathsize 12px style straight s equals 1 half open parentheses straight v plus straight u close parentheses straight t end style ....... (Equation 1)
From the first equation of motion, v = u + at;
begin mathsize 12px style straight t equals fraction numerator straight v minus straight u over denominator straight a end fraction end style
Substituting in equation 1, we get
begin mathsize 12px style straight s equals 1 half open parentheses straight v plus straight u close parentheses fraction numerator open parentheses straight v minus straight u close parentheses over denominator straight a end fraction end style
or, v2 – u2 = 2as
Explanation:
