Question

A particle moves 4m towards South and then it moves 3m towards West. The total time taken by the particle is 2 seconds. What is the ratio of its average speed and average velocity? Ibis 5 7 14 5 a) b d) 7 5 14 So- Sen b) 1 / c) (n.) - د) nied the



with explanation ​

Answer 1

Given:

Total Distance(d) = 4m + 3m

                            = 7m

Total Time(t) = 2s

To Find:

The ratio of Average Speed & Average Velocity

Solution:

For Average Speed,

Formula is,

                $Average Speed = \frac{Total Distance}{Total Time}$

                $Average Speed= \frac{7}{2}$

                $Average Speed=3.5 m/s$

For Average Velocity,

First, the displacement should be calculated.

Since the particle's path is at 90°. So, the displacement will be the hypotenuse of the triangle formed by the path.

Let us assume the movement towards South as 'p',

                        the movement towards West as 'b'

                        And, the displacement as 'h'

                                            $h^{2}= b^{2}+ p^{2} \\h^{2}= 3^{2}+ 4^{2} \\h^{2}=9+16\\h^{2}=25\\h=\sqrt{25} \\h=5$

By using this displacement,

                       $Average Velocity = \frac{Total Displacement}{Total time}$

                       $Average Velocity = \frac{5}{2} \\Average Velocity = 2.5$

Now the ratio,

                                      $Ratio = \frac{Average Speed}{Average Velocity} \\Ratio = \frac{3.5}{2.5}$

                                      $Ratio = \frac{7}{5}$

                                    Ration = 7 : 5