Question

An object starts with initial velocity u and attains final velocity v. The velocity is changing at a uniform rate. What is formula for calculating average speed in this situation ?

Answer 1

Let initial velocity is u and final velocity is v. Velocity is changing uniformly.

This means that the motion is uniformly accelerated.

Let acceleration be f.

Also, let distance traveled be s.

So, v² = u² + 2fs So, s = (v² - u²)/2f -----(1) Also, v = u + ft So, t = (v-u)/a -----(2)

Now, Let average speed be V(avg).

Then V(avg) = Total Distance/Total Time So, V(avg) = s/t So, V(avg) = [(v²-u²)/2a] ÷ [(v-u)/a]

From equation (1) and (2)

So, V(avg) = [(v+u)(v-u)/2] ÷ (v-u) So, V(avg) = (v+u)/2.

Thus, the average speed is the average of initial and final velocities in this case.

Answer 2

Answer: The formula for calculating average speed in this situation is v+u/2.

Explanation:

As the initial velocity = u

And the final velocity = v

In time (T)

So at =$(\frac{v-n}{t} )$

As the average velocity = total average travelled / total time

As we know, the total time = t,

So, now s = ut + 1/2 at²

                =ut + 1/2 (v-n/t)t²

                =ut + 1/2 (v-n)t

                =ut + vt/2 - ut/2

                =vt/2 + ut/2

∴ V average = $\frac{\frac{vt}{2} +\frac{ut}{2} }{t}$

                     =$(\frac{v+u}{2} )$

Hence, The formula for calculating average speed in this situation is v+u/2.

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