Question

Derive the equation of uniformly accelerated linear motion using algebraic method.

Answer 1

Answer:

Derivation of uniformely accelerated linear motion by using algebraic method.

Answer 2

Equations of motion

Explanation:

Given that a body is travelling at uniform acceleration along a straight line with initial velocity u and final velocity v at time t.

Acceleration a = v-u / t

at = v - u

v = u + at ----------------------------  (1)

Distance s = velocity * time  

s = (u+v)/2 * t

s = (u + u + at) /2 * t

s = (2u/2 + at/2)t

s = ut +1/2*at^2 -------------------- (2)

Squaring both sides of equation 1, we get:

v^2 = (u+at)^2

 = u^2 + a^2t^2 + 2uat

 = u^2 + 2a (ut +1/2 at^2)

v^2 = u^2 + 2as ---------------------- (3)

Thus we have 3 equations of motion.