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Constant Velocity

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When the body moves with a constant speed in a fixed direction we say that the body is moving with constant velocity. An automobile traveling on a straight, flat highway at a constant speed is a good example for constant velocity. In this section we will learn more about constant velocity.

What is Constant Velocity?

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When a body travels in a straight line and covers equal distance in equal intervals of time, it is said to have constant velocity. Thus, a body is said to have constant velocity if it covers equal distance in equal intervals of time, and in a straight line.

For example, a car travelling with a constant speed in a straight line has constant velocity.

Constant Velocity Equation

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When the instantaneous velocity of a body does not change, it is moving at a constant velocity. For the case of constant velocity, the basic formula $v = \frac{s}{t}$ can be rewritten to give the distance covered in a given period of time:

$Distance$ = $Constant\ velocity \times time$

$s = v \times t$


Another way to write $v$ = $\frac{s}{t}$ gives the time need to cover a given distance at the constant velocity $v$:

$Time$ = $\frac{Distance}{Constant\ Velocity}$

$t$ = $\frac{s}{v}$

Constant Velocity Graph

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The velocity-time graph for constant velocity is shown below. Which is a horizontal line parallel to the x- axis. The slope of the graph is zero. That is the acceleration of an abject moving with constant velocity is zero.

Constant Velocity Graph

Examples of Constant Velocity

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The following are the problems of constant velocity.

Solved Examples

Question 1: A car moving with a constant velocity of 160 kmh-1. How do you calculate the distance travelled by the car in 36 s?
Solution:
 
Given,

Velocity = $160$ kmh-1 = $160 \times$ $\frac{5}{18}$ ms-1 = $\frac{400}{9}$ ms-1

Time taken = $36$ s

The formula for velocity = $\frac{Distance\ travelled}{Time\ taken}$

        $Distance$ = $Velocity \times Time$

                      =  $\frac{400}{9}$ ms-1 $\times 36$ s

                     = $1600$ m
                   
                     = $1.6$ km

 

Question 2: In a 1000 metre race, the winner takes 20 seconds to reach the finishing point. Calculate the the velocity of the winner.
Solution:
 
Given,

Displacement = $1000$ m

Time= $20$ s

Then the velocity of the winner = $\frac{Total\ distance\ travelled\ along\ a\ straight\ line}{Total\ time\ taken}$

                           = $\frac{1000}{20}$

                           = $50$ m/s   

The velocity of the winner is $50$ m/s.

 

Question 3: How do you calculate the constant velocity of bus which has the displacement 200 metre with 10 seconds?
Solution:
 
Given,

Displacement of bus = $200$ m

Time taken = $10$s

Then the velocity = $\frac{Displacement}{Time}$

                             = $\frac{200}{10}$

                             = $20$ m/s

The velocity of bus is $20$ m/s.