Question

A particle moving in a straight line path covers half of the total distance at speed of 3m/s the other half distance is covered in two half equal intervals of time with speed 4.5m/s and 7.5m/s .Find the average speed of this particle

Answer 1

Question 32639

Let the total distance be $L$. Then particle has moved $L/2$ at velocity $v_1 = 3m/s$, $L/4$ at velocity $v_2 = 3.5\frac{m}{s}$ and $L/4$ at velocity $v_3 = 7.5\frac{m}{s}$.

Average velocity is $v = \frac{L}{t}$, where $t$ is the time needed to cover the whole distance.

Time to travel each distance is (knowing the velocities):

$$t_1 = \frac{\frac{L}{2}}{v_1}; \quad t_2 = \frac{\frac{L}{4}}{v_2}; \quad t_3 = \frac{\frac{L}{4}}{v_3}.$$

Total time is $t = t_1 + t_2 + t_3$.

Therefore, average velocity is $v = \frac{L}{t} = \frac{\frac{L}{2v_1} + \frac{L}{4v_2} + \frac{L}{4v_3}}{2v_1 + \frac{1}{4v_2} + \frac{1}{4v_3}} = \frac{90}{23}\frac{m}{s} \approx 3.91\frac{m}{s}$.