KINEMATICS - ACCELERATION

KINEMATICS -ACCELERATION
TYPES OF ACCELERATION
There are different types of accelerations are there. Out of those, some of the types we will discuss here.
1.    Positive Acceleration
2.    Negative Acceleration
3.    Zero Acceleration
4.    Uniform Acceleration
5.    Non-Uniform Acceleration
6.    Average Acceleration
7.    Instantaneous acceleration
Positive Acceleration:
    When the motion of the body is in same direction as that of acceleration, we say the acceleration is positive. In another terms, if initial velocity (U) is less than final velocity (V), then it is called as positive acceleration. (U     Ex:A bus or car moving with increasing speed has positive acceleration. We can say that it is accelerating with the direction of travel.
Negative Acceleration:
    When the motion of the body is opposite to the direction of acceleration, we say the acceleration is negative. In another terms, if initial velocity (U) is greater than final velocity (V), then it is called as negative acceleration. (U>V)
Ex:A bus or car moving with increasing speed, then if we apply the break, the speed of  the car decreases. Then it has negative acceleration. So we can say that it is decelerating.
Zero Acceleration:
    If the acceleration is zero, it means that the velocity is steady, not increasing or decreasing in magnitude. If the object has zero velocity and zero acceleration, it is stationary and not changing that stationary condition.
    Ex:An apple thrown in space, in space that apple can’t change its velocity, so no  acceleration exists for it.
Constant acceleration means that the acceleration does not change. If the acceleration is zero then the acceleration does not change, so we can say that the body is moving with uniform velocity.
Uniform Acceleration & Non-Uniform Acceleration:
    If an object’s speed (velocity) is increasing at a constant rate then we say it has uniform acceleration. The rate of change of acceleration is constant.This acceleration is the same over time. If a car speeds up then slows down then speeds up it doesn’t have uniform acceleration. This is called non-uniform acceleration.

Average Acceleration:
    Acceleration is the rate of change for velocity, that is, change in velocity over a specified period of time. Average acceleration is the final velocity minus the initial velocity per time taken.
\(Average\,Acceleration\,{A_{avg}} = \frac{{\Delta v}}{{\Delta t}} = \frac{{change\,in\,velocity}}{{change\,in\,time}} = \frac{{{v_f} - {v_i}}}{{{t_f} - {t_i}}}\)
Example 2:
Your friend’s new car can go from 0 to 60 m/s in 7 sec. What is the acceleration?
Solution:
    The final velocity, V_f = 60 m/s;     The initial velocity, V_i = 0 m/s; 
    The final time, T_f = 7 sec;        The initial time, T_i = 0 sec;
     \({A_{avg}} = \frac{{\Delta v}}{{\Delta t}}\)= (60 m/s) / 7 s= 12.86 m/s²
Example 3:
    When driving along a side-road at 45 m/s, you see a child run out into the street, and rapidly slow to 3 m/s, within 1.5 sec. What is your acceleration?
Solution:
The final velocity, V_f= 3 m/s; the initial velocity, V_i= 45 m/s; and the time,  t = 1.5 sec.
    \({A_{avg}} = \frac{{\Delta v}}{{\Delta t}}\)= (3 m/s - 45 m/s) / 1.5 sec= (- 42 m/s) / 1.5 sec= - 28 m/s²
Notice, the negative sign, indicating the object slowed down.
Example 4:
A bus accelerates with an initial velocity of 10 m/s for 5s then 20m/s for 4s finally for 15 m/s for 8s. What can be said about the average acceleration of the bus?
Solution:
    It is given that, the velocities of the bus at different time intervals is, 
V₁ = 10 m/s, V₂ = 20m/s, V₃ = 15m/s
    The time intervals for which the object possesses these velocities are t₁ = 5s,t₂ =  4s, t₃ = 8s
Hence, over the interval, the total velocity can be given as the sum of these velocities.
\(\Delta v\)=10+20+15=45m/s
Similarly, the total time interval can be given as the sum of these intervals,
\(\Delta t\)=t₁ +t₂+t₃=5+4+8=17s
Using the above formula for average acceleration, we get,
    AverageAcceleration=\(\Delta v\)/\(\Delta t\)
    Average Acceleration=45/17=2.65ms^-2
Instantaneous Acceleration:
When an object is moving with variable acceleration, then acceleration of the object at any instant of time is called instantaneous acceleration. It may be also defined as the limiting value of average acceleration over an interval of time, which approaches to zero.In the above diagram, car have zero initial velocity, after that car started moving.

At different instants of time, different accelerations are mentioned in the above diagram. This above diagram shows  that non uniform accelerated motion also.
Get clarity here:
The change of velocity over an instance of time. Constant or uniform acceleration is when the velocity changes the same amount in every equal time period.