# Uniform Acceleration and Non-uniform Acceleration

**If the velocity of an object is changed from one point to another either in magnitude or direction , This change in velocity with time is known as acceleration and such motion is called accelerated motion . **

**Acceleration is the change of the object velocity per unit time or it is the rate of change of velocity , Accelerated motion is the motion in which velocity changes with time , Acceleration of motion can be found by the relation :
**

**Acceleration = Change in velocity / Time of change **

**Acceleration = ( Final velocity − Initial velocity ) / ( Final time − Initial time )**

**a = Δ v / Δ t = ( v _{2} − v_{1} ) / ( t_{2} − t_{1} )**

**The unit of measuring acceleration is m/s² or km / h² and its dimensions LT ^{−2} , You can convert the unit of measuring acceleration from km / h² into m / s² as follows : **

**1 km / h² = 1 km / ( 1 h )² = 1000 m / [ ( 60 × 60 ) s² ] = 5 / ( 18 )² m / s²**

**Types of Acceleration **

**Uniform Acceleration**

**It is the acceleration in which the object changes its velocity with equal intervals of time .**

**Non-uniform Acceleration**

**It is the acceleration in which the object changes its velocity with unequal intervals of time .**

**The acceleration may be positive acceleration ( increasing velocity ) , Zero acceleration ( uniform velocity ) , Negative acceleration and in this case it is called deceleration ( decreasing velocity ) .**

**When the velocity of object increases with time , This is called positive acceleration , when the velocity of object is constant with time , This is called zero acceleration , when the velocity of object decreases with time , This is called negative acceleration . **

** Positive acceleration **

**It is the acceleration of the object when its velocity increases with time , Example : As the ball rolls down the inclined plane .**

**Zero acceleration **

**It is the acceleration when the velocity of object is constant with time , Example : as the ball moves along the smooth horizontal plane .**

**Negative acceleration**

**It is the acceleration of the object when its velocity decreases with time , Example : As the ball climbs up the inclined plane . **

**Graphical representation**

**When plotting the graphical relationship of ( velocity – time ) we may get :**

**A straight line that may start from the origin , By finding the slope of the straight line , we obtain the acceleration of the object motion , when the slope of line is positive , It is a positive acceleration , The object is moving at a uniform acceleration .**

**A straight line parallel to the time axis , It is zero acceleration , The slope of line = 0 , The object is moving at zero acceleration .**

**A straight line that may end at the time axis , The slope of line is negative , It is negative acceleration , The object is moving at a uniform deceleration . **

**The projectile whose velocity decreases till reaches zero at its maximum height , represents an example for negative acceleration .**

**When the object moves at a uniform acceleration = 10 m/s² , It means that the object velocity increases by 10 m/s every second .**

**When an object decelerates uniformly at − 10 m/s² , It means that the object velocity decreases by 10 m/s every second .**

**Guidelines to solve problems **

**To solve the problems of acceleration , use the diagram :**

**Where Δ v is the change in velocity which determined by the relation : Δ v = v**_{f}− v_{i}.**If the object moves at uniform velocity , its acceleration of motion = zero because Δ v = zero .****When the object starts motion from rest , its initial velocity ( v**_{i}) = zero .**When the object comes to rest , its final velocity ( v**_{f}) = zero .**When the final velocity ( v**_{f}) > the initial velocity ( v_{i}) , acceleration is positive .**When the final velocity ( v**_{f}) < the initial velocity ( v_{i}) , acceleration is negative .**When the final velocity ( v**_{f}) = the initial velocity ( v_{i}) , the acceleration is zero ( uniform velocity ) .**If the velocity and acceleration have the same direction then they have the same sign ( Acceleration motion ) .****If the velocity and acceleration have opposite direction then they have the opposite signs ( Decelerating motion ) .**

**Notes**

**The meaning of ( − ve ) sign for : **

**Displacement : The body moves in opposite direction .****Velocity : The body moves in opposite direction .****Δ v ( change in velocity ) : The velocity of the body decreases .****Acceleration : The velocity decreases or acceleration is in opposite direction to velocity .**

**Time is never written with negative value as it is a scalar quantity .**

**Safety skills , Applications of motion with uniform acceleration ( Free fall & Projectiles )**

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