Question

Give the formulae to be used to calculate average velocity when the motion of the body is.
a) uniformly accelerated
b) non-uniformly accelerated.

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Answer 1

Answer:

a) uniformly accelerated

The three equations are, v = u + at. v² = u² + 2as. s = ut + ½at²

b) non-uniformly accelerated.

the equation a(t) = 15t.

Explanation:

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Answer 2

→ The average velocity of a body is equal to the net displacement per unit time.

→ The base or fundamental formulae to calculate the average velocity remains the same in case of (a) Uniformly accelerated motion as well as (b) Non-uniformly accelerated motion:

→ The fundamental formulae for the average velocity is given as Net displacement (S) divided by the total time (ΔT).

                          $Avg. Velocity=\frac{Net Displacement( S)}{Time(\triangle T)}$

→ In case of (a) Uniformly accelerated motion:

Let the uniform acceleration be 'a'

Let the initial and final velocities be 'u' and 'v' respectively.

Therefore by the Second equation of motion, the Net Displacement (S) is given by:

                                       S = ut + 1/2(at²)

                           $Avg. Velocity=\frac{NetDisplacement(S)}{Time(\triangle T)}= \frac{S}{t}$

                           $Avg. Velocity=\frac{ut+\frac{1}{2}at^{2} }{t} =u+\frac{1}{2}at$

→ By First equation of motion that is  v = u + at, we get: (v-u) = (at)

                        $\therefore Avg. Velocity=u+\frac{1}{2} (v-u)$

                           $Avg. Velocity=\frac{2u+v-u}{2} =\frac{v+u}{2}$

                         ∴ Average velocity = (v + u)/2.

→ Hence in the case of uniformly accelerated motion the average velocity is the average of Final velocity (v) and initial velocity (u).

→ In the case of (b) Non-uniformly accelerated motion:

→ In the case of Non-uniformly accelerated motion, the base formulae remains the same: Here also the average velocity is equal to Net displacement (S) divided by the total time (ΔT).

But here would calculate the Net displacement through integration or summation. Dividing the Net displacement by the total time taken would give us the average velocity in this case.

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