Question in motion?

Question

when a particle moves with constant velocity its average velocity .its instantaneous velocity and speed are equal. Comment on this statement

Answer 1

S = constant speed; so s1 = S and s0 = S; thus average speeds s = (s1 + s0)/2 = 2S/2 = S. s0 is the initial instantaneous speeds and s1 the final. The average speed, which is a scalar, is just the sum of the two instantaneous speeds divided by 2. (The average of any set of scalar numbers is just the sum of the numbers divided by the quantity of numbers.)

Since both instantaneous speeds are S and the average is S then is it clear that the average and instantaneous speeds are the same value. BUT, and this is a big but, what about the velocities?

Velocity is speed with direction. Thus, in general, we can say the sum of two velocities is a vector sum, not a scalar sum like we did for the two instantaneous speed. In which case, we need to know the directions of the two instantaneous velocities v1 and v0.

For example, if v0 is going 60 mph west and v1 is going 60 mph east, the sum of those two instantaneous velocities is 120 mph…right? No…wrong…the sum of these two velocities, because they are going in opposite directions, is zero. Thus v = (v1 + v0)/2 = 0/2 = 0; and the average velocity is zero…nada.

Zero, after traveling 60 mph in both directions? Why not 60 mph? Think about it. Say you drive an hour at 60 mph west to Podunk in your car. In Podunk you realize you forgot your billfold and the driver's license inside. So you turn around and drive 60 mph back to pick up your billfold.

What was your average velocity...60 mph? Nope. Look where you are after two hours driving...you're back home.

Distance traveled after two hours...zero miles, you are back where you started from. Thus v = distance/time = 0/2 hours = 0, which is your average velocity because you traveled no net distance after two hours. You see, distance is also a vector and the sum of the two distances, to and from Podunk, is zero.

On the other hand, if both v1 and v0 were going west, what would the sum be then if V = constant velocity? It would be 2V; so that the average velocity would be v = 2V/2 = V if and only if the two instantaneous velocities were in the same direction.

So what’s the major comment…direction matters with velocity, it doesn’t matter with speed.

Answer 2

Since it is moving vid constant speed its velocity ia any two different instants remain constant (same) thus its instantaneous velocity nd speed are equal to its average velocity(which is calculated as the average of velocity of some instants divied by those instant )

www.i-search.co.in

Answer 3

as velocity of particle is constant.i.e. it covers equal distances in equal interval of time. thus when total displacement divided by total time of motion its result is same as its instantaneous velocity. IN ONE DIMENSIONAL MOTION WHEN PARTICLE DOESNOT CHANGES ITS DIRECTION THEN ITS DISPLACEMENT AND DISTANCE TRAVELLED ARE EQUAL.NOW WE CAN SAY ITS SPEED AND VELOCITY BOTH ARE EQUAL. thanks.