Question

a body stars with a speed of 50 km/h and after travelling for 30 minutes it attended the speed of 100km/h now calculate average speed of the body

Answer 1

Solution.

A body stars with a speed of $50~\mathrm{km/h}$ and after travelling for 30 minutes it attended the speed of $100~\mathrm{km/h}$ now calculates average speed of the body.

$$v_0 = 50 \frac{\mathrm{km}}{\mathrm{h}}$$ $$v = 100 \frac{\mathrm{km}}{\mathrm{h}}$$ $$t = 30 \min = \frac{1}{2} \text{ hour}$$

Obviously, the body is moving with some acceleration. Let's find it:

$$v = v_0 + a t$$ $$a = \frac{v - v_0}{t} = \frac{100 \frac{\mathrm{km}}{\mathrm{h}} - 50 \frac{\mathrm{km}}{\mathrm{h}}}{\frac{1}{2} \mathrm{h}} = 50 * 2 = 100 \frac{\mathrm{km}}{\mathrm{h}^2}$$

Secondly, to find average speed we need to find the distance:

$$S = v_0 t + \frac{a t^2}{2}$$ $$S = 50 * \frac{1}{2} + \frac{100 * \frac{1}{4}}{2} = 25 + 12.5 = 37.5 \mathrm{km}$$

The total distance, that body had travelled is $37.5~\mathrm{km}$.

And now to find the average speed:

$$v_{AV} = \frac{S_{total}}{t} = \frac{37.5 \mathrm{km}}{\frac{1}{2} \mathrm{h}} = 75 \frac{\mathrm{km}}{\mathrm{h}}$$

Answer: $75 \frac{\mathrm{km}}{\mathrm{h}}$