Question

how to derive equations of motion by algebraic method​

Answer 1

Explanation:

First, consider a body moving in a straight line with uniform acceleration. Then, let the initial velocity be u, acceleration be a, time period be t, velocity be v, and the distance travelled be S.

Answer 2

Answer:

The following are the kinematic equations of a body uniformly accelerated:

• v = u + at
• s = ut + 1/2 at²
• v² - u² = 2as

Derivation of the first equation by algebraic method -

Let us assume a body to be in uniform acceleration "a" whose initial velocity is u and the final velocity of the body is v at time t.

We know that, Acceleration = (v - u)/t.

⇒ a = (v - u)/t

⇒ at = v - u

⇒ v = u + at

Derivation of the second equation by algebraic method -

We know that, Average velocity = (u + v)/2.

We know, Distance traveled = Avg. speed * time

⇒ s = (u + v)/2 * t

⇒ s = (u + u + at)/2 * t

⇒ s = (2u + at)/2 * t

⇒ s = (2ut + at²)/2

⇒ s = 2ut/2 + at²/2

⇒ s = ut + 1/2 at²

Derivation of the third equation by algebraic method -

We know, a = (v - u)/t

⇒ t = (v - u)/a

Using second equation of motion :

⇒ s = ut + 1/2 at²

⇒ s = u [(v - u)/a] + 1/2 a[(v - u)/a]²

⇒ s = (uv - u²)/a + a(v² + u² - 2uv)/2a²

⇒ s = (uv - u²)/a + (v² + u² - 2uv)/2a

⇒ s = (2uv - 2u² + v² + u² - 2uv)/2a

⇒ s = (v² - u²)/2a

⇒ 2as = v² - u²