Question

which is greater 3m/s or 3km/hr?

how will the equation of motion for an object moving with uniform velocity change?

is the motion of a body uniform or accelerated, if it goes around the sun with constant speed in circular orbit?

Answer 1

Hey There!

Let us take all the questions in order:

1) Which is greater 3m/s or 3km/hr?

To answer this question, we first need to bring both of them in the same units. 

Let us convert 3 km/hr into metres per second.

Now,

$3\, \, km / hr \\ \\ \\ = 3 \frac{km}{hr} \\ \\ \\ = 3 \times \, \frac{1000 \, m}{60 \times 60 \, s} \\ \\ \\ = 3 \times \frac{1000}{3600} \, \frac{m}{s} \\ \\ \\ = 3 \times \frac{5}{18} \, \, m / s \\ \\ \\ \approx 0.83 \, \, m / s \\ \\ \\ \implies \boxed{3 \, km / hr \approx 0.833 \, \, m / s}$

Clearly, 0.833 m/s is a lot less than 3 m/s.

So, we have our answer: 3 m/s is greater than 3 km/hr


2) How will the equations of motion for an object moving with uniform velocity change?

We are given that the object is moving with uniform velocity. This means that the velocity does not change. This means that the acceleration is zero. 


We put a=0 in all the equations.

Let us take our three equations:

$a) \, v = u<em> + </em>at \\ \\ \implies v = u + 0 \\ \\ \implies \boxed{v=u}$


$b) \, s = ut + \frac{1}{2}at^2 \\ \\ \implies s = ut + \frac{1}{2}(0)(t^2) \\ \\ \implies \boxed{s=ut}$


$c) \, v^2 = u^2+2as \\ \\ \implies v^2 = u^2 + 0 \\ \\ \implies v^2=u^2 \\ \\ \implies \boxed{v=u}$



So this was how our equations change when acceleration is zero, i.e. body is moving with uniform velocity.


3) Is the motion of a body uniform or accelerated, if it goes around the sun with constant speed in circular orbit?


The first thing we need to remember is that velocity and acceleration both are vector quanitites. The direction of motion is of utmost importance if we want to know velocity. 

In a circular path when speed is constant, the body is moving along a curve. The direction of body is changing at each instant.

In our case, we are given that the Earth goes in a circular orbit around the Sun. The direction of motion of Earth is changing at each instant. 
This means that the velocity of the Earth is changing, simply because the direction of motion is changing.

And then, Acceleration is the rate of change of velocity. So, if Earth's velocity is changing, then it must have acceleration.

Thus, Motion of Earth around the Sun is accelerated.
This acceleration is in fact known by a special name, and it is known as Centripetal Acceleration.



Hope it helps
Purva
Brainly Community