Question

a point moves with uniform acceleration and its initial speed and final speed are 1 m/s and 2 m/s respectively then the space average velocity over the distance moved is ?

Answer 1

Concept:

Here we will use the concept of average velocity and simultaneously we will use the equations of motion.

Average Velocity = Total Displacement(s) / Total Time (t)

Also,

First Equation of Motion: $v=u + at$

Second Equation of Motion:$s=ut+\frac{1}{2} at^{2}$

Given:

Initial Speed = 1 m/s

Final Speed= 2 m/s

Find:

To find the average velocity.

Solution:

As we know that average velocity = Total displacement (s)/Total time (t)

                                                                            ----------------------equation (1)

and from second equation of motion we have

s= ut+ 1/2 $at^{2}$ , putting this value in equation (1)

Now , we have

average velocity =$\frac{ut+\frac{1}{2} at^{2} }{t}$

average velocity = u+1/2 at--------------equation (2)

and from first equation of motion

we have v=u + at

Therefore, at= v- u

Now, putting this value in equation (2)

Average velocity = u+ 1/2 (v-u)

Now putting the value of u and v i.e. u= 1m/s, v= 2m/s

Average velocity = 1+ 1/2(2-1)

                             = 1+1/2

                             =3/2 = 1.5 m/s

Hence, the average velocity is 1.5 m/s.

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