Sunday, February 17

Algebra Velocity

Introduction:

Algebra  was popularized in near the beginning ninth century by al-Khowarizmi. The author of the first algebra book was preferred by , Al-jabr wa'l Muqabalah, from which the English word algebra is derived. It remained the standard text in algebra for a long time. The title translates almost to "restoring and balancing, " referring to the primary algebraic method of performing an operation on one side of an equation and restoring the balance, or equality, by doing the same thing to the other side.


Definition:

Velocity  can defined as vector measurement of the rate and direction of movement or, in other terms, the rate and direction of the change in the position of an object. The scalar  magnitude value  of the velocity vector is the speed of the motion. In mathematical terms, velocity is the first derivative of position with respect to time.

More about velocity:

1)  Velocity is a vector quantity.

2)  It is also defined as the distance per unit time, i.e.,  if  s  is distance traveled in time t, then velocity

3)  m/sec,cm/sec,ft/sec,km/hr,miles/hr etc.

4)  Velocity V =  ds / dt

.             Here,

s – Position vector

ds – First derivative of Position vector

t –  time

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Examples:

1. Find the velocity of Ed . it covers a distance of 225 miles in 5 hrs..

velocity   V  = 225 / 5   miles/sec.

velocity   V =45 miles/sec.

2. A submarine descends -120 ft in 6 seconds. What is the velocity of the submarine?
Choices:
A. 30 ft per second
B. - 30 ft per second
C. - 20 ft per second
D. 20 ft per second
Correct Answer = C
Solution:

Step 1:  Velocity = Displacement nt / time .

Step 2:  Since  submarine is descending, the displacement will be negative.

Step 3:  Displacement =120 ft and Time = 6 sec

Step 4:  velocity = -120 / 6 [Substitute the values of displacement and time.]

Step 5:  velocity = 20 [Divide.]

Step 6:  So, The velocity  = - 20 ft / second.


Velocity terms:

Displacement
Distance
Position
Rate
Rate of Change
Speed
Time
These are the various terms involved in velocity.

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