Showing posts with label The Velocity. Show all posts
Showing posts with label The Velocity. Show all posts

Wednesday, April 24

Initial Velocity

Let us start with the difference between velocity and speed. It is quite obvious after all the discussion about vector and non vector quantities. Speed is basically a measurement with no direction. In case of velocity we also consider direction.

Velocity can be of two types: initial velocity and final velocity. When the object starts its motion then we can say that the initial velocity is zero as it has just started from rest. Similarly we can also consider int. velocity as some constant value. Let us take an example of a car starting from rest and attaining a velocity of 50 km per hour in 1 hour time period.

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So here we can say that the int. velocity of the car is zero and the final velocity is 50 km per hour, directed northwards. Here mentioning the direction is very important as velocity is all about direction, it being a vector quantity.

Let us now discuss Initial velocity formula. We have 3 equations of motion that have a reference to int. velocity and hence can be used for its calculation.
They are as follows:
V = u + a t ------------ > (1)
Here v is the final velocity
U is the int. velocity
A is the acceleration
T is the time period.
So u = v – a t
Also the second equation is
S = u t + 1.5 a t^2 - - - - - - >(2)
Here s is the distance covered in time interval t.
A is the acceleration
We also have a third equation for calculating velocity. It is as follows:
V^2 = u^2 + 2 a s - - - - - - -> (3)

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Here v is the final velocity and a is the initial velocity.
All these are initial velocity equation. We can also say that u^2 = v^2 – 2 a s - - - - - - - > (4)
Let us take a real world example to clear the concept. Let us assume the final velocity of the car is 50 m per sec and the time taken to complete the journey is 2 hours. Also the acceleration is 10 meter per second square. So now using first formula we will try to calculate the initial velocity.
Hence v = u + a t
Or 50 = u + 20
U = 50 – 20 = 30 m per sec

Friday, March 22

Initial Velocity

The first question that arises when we read about distance, speed and velocity is the basic difference between speed and velocity. Velocity is the directional quantity while speed is not. We have already discussed about the importance of direction while calculating vector quantities.Having problem with Formula for Velocity keep reading my upcoming posts, i will try to help you.

Velocity in simple terms can be defined as the distance covered per unit time in a particular direction. This means that here we are also taking the direction in consideration. If we were to define speed we could have said it the distance per unit time. We will not have mentioned the direction bit.

We can divide the velocity into two parts. These are final and the initial velocity. As it is clear from the name the In. velocity is basically the starting velocity of an object or a body while final velocity is the finishing velocity. It may seem confusing at first but is quite easy.

Let us take an example. If the car starts and attains a velocity of 30 kilometers per hour then the initial vel. Considered would be zero km per hour while the final velocity will be 30 km per hour after 4 hours in a particular direction say southwards. Calculate Initial Velocity is easy. We can directly use the equation of motion which says
v = u + a t - - - - - - -(1)
Here v is the final velocity
U is the initial velocity
A is the acceleration
And t is the time taken to attain the final velocity.
Also s = u t + ½ a t 2 - - - - - - - - -(2)
Here s is the distance covered in a particular time interval.
This is the Equation for Initial Velocity. There is yet another equation for its Calculating Initial Velocity. It is:
V2 = u2 + 2 a s - - - - - - - - - - -(3)
Let us assume a ball is rolling on a platform. It attains a velocity of 10 m per seconds with an acceleration of 4 m per second 2. The time taken is 2 seconds.
Let us try to calculate the initial velocity.  Take the first equation into consideration.
So v = u + a t
10 = u + 2 * 4
10 = u + 8
u = 2
So initial vel. is  2 metre per second.
You can also calculate it according to different values of s, a, v, t in different situations.

Wednesday, February 13

Uniform Motion

Introduction to Uniform Motion

A motion is said to be uniform if the particle covers equal distances in equal intervals of time, however  small these intervals of time may be , always in the same direction. Strictly speaking , no motion is uniform.

When a particle has uniform motion, neither the magnitude nor the direction of velocity changes , so the velocity is constant in uniform motion and is equal to Instantaneous velocity of the particle. I like to share this equation for frequency with you all through my article.

So uniform is a relative concept. If an object A is in uniform motion relative to another object B, then from B's view there appear to be no force applied to A; i.e. it appears to be neither accelerating nor decelerating, nor changing directions or moving in a curve. The same should apply vice versa.

when a particle possess uniform motion, it's velocity- time graph is a straight line parallel to time axis.If the velocity of the particle is taken as positive, the straight line is taken above the time axis and if it is negative, then the V-t graph will be a straight line below the time axis

Uniform Motion : Velocity- time Graph

The Velocity- time graph for uniformly accelerated rectilinear motion is straight line sloping upwards.

The velocity- time graph for a uniformly retarded motion is a straight line sloping downwards.

Let us consider a particle moving with constant acceleration .If U and V be the velocities at time t1 and t2  respectively, then

`V= U+at` gives the equation connecting initial velocity, final velocity, acceleration and time. I have recently faced lot of problem while learning Effects of Radiation on Humans, But thank to online resources of math which helped me to learn myself easily on net.

Uniform Motion : V-t Graphs and Acceleration

The Velocity- time graph for the uniformly accelerated motion of a particle is a straight line sloping upwards.

The area under the V-t graph gives the distance covered by the particle.It is calculated by the equation `V^2= U^2+2ad`

so here distance is as area under Velocity- time graph

The slope of the V- t graph for uniformly accelerated motion gives the acceleration.