Deceleration Formulas with Solved Examples
Deceleration is a very commonly occurring phenomenon in our daily lives. Anytime we are travelling, we may notice in the vehicle that when we feel moving forward relative to the vehicle, then we are experiencing Deceleration (a slow down of our Velocity). Here, Deceleration is to be considered as a special case of Acceleration whereby it only applies to objects slowing down. In short, it is the rate at which an object slows down.
Acceleration is a Vector attribute of an object in Motion. This is because of two components : a magnitude and a direction. To denote the direction in cases of one-dimensional Motion, negative and positive signs are used. Thus, if the signs are negative then the object is decelerating or is said to be in retardation.
Deceleration can be understood as the opposite phenomenon of Acceleration. The Deceleration can be calculated by dividing the final Velocity minus the initial Velocity, by the amount of time taken for this drop in Velocity. The formula for Acceleration must be used here, with a negative sign, to identify the Deceleration value.
Deceleration, also known as retardation or negative Acceleration, is the Acceleration acts in the opposite direction of Motion and is responsible for reducing the Velocity of a body.
Deceleration(a) = \[\frac{final velocity - initial velocity}{Time}\]
If, u = initial Velocity
v = final Velocity
a = constant Deceleration
t = time taken
and
s = displacement
Then equations of Motion is given by:
v = u - at
s = ut - ½ at2
v2 = u2 - 2as
SI unit of Deceleration is m/s².
Example:
An object moving with a Velocity of 40m/s is brought to rest in 8 seconds by a constant Deceleration. Find the Deceleration applied.
Ans:
Here, initial Velocity(u) = 40m/s
Final Velocity(v) = 0 m/s
Deceleration = a
Time = 8 s
From 1st equation of Motion:
v = u - at
0 = 40 - a.8
a = 40/8
= 5 m/s².
Question:
If an object is accelerated from rest with an Acceleration of 2 m/s² for 10s, How much Deceleration is needed to bring the object to rest in 4s.
Deceleration in Gravity Units (G’s)
To calculate Deceleration rate when an object is under the influence of gravity, and if one desires to obtain the result in terms of gravity units (G), one of the two methods described here can be used.
First Method:
Divide the Deceleration by the standard gravitational Acceleration (the value of which is 9.8m/s²). The result gives the average number of G’s applied to the moving object to achieve the Deceleration.
We can understand this with the help of an example: Find the G Force required to stop the car with Deceleration equal to -27.66 feet per second square
The calculated Deceleration for the moving car is 27.66 feet per second per second. The Deceleration is equivalent to:
27.66/32 = 0.86 G’s
Determining Deceleration Using Speed Difference and Time
This is quite simple. First subtract the ending speed from the starting speed.
Convert the speed difference to units of speed that are compatible with the Acceleration to be calculated, usually metre per second. If the speed is in miles per hour, convert that speed to metres per second by multiplying kilometers per hour by 0.278.
Then, divide the speed change from the time during which the change occurred. This calculation gives us the value of the average Deceleration rate.
Determining Deceleration Using Speed Difference and Distance
Convert the initial and final speeds to units that will be useful for calculating the Acceleration (meters per second).
Next, square the initial and final speeds.
Subtract these squares obtained in the previous step as: square of the final speed minus the square of the initial speed.
Divide by two times the distance. This is the average Deceleration rate.
FAQs on Deceleration Formula
1. What do we mean by Deceleration of an object?
Deceleration is an attribute of a moving object. It literally means “reduce Acceleration”. That is, as the object slows down, it’s rate of change of Velocity is found to be negative (meaning, the Vector quantity is decreasing in value). This causes the object to finally achieve zero Acceleration. In most cases the object in Motion comes to rest. This also implies that a moving object can not abruptly come to inertia without an aspect of change of rate of Velocity.
2. What formula is used to calculate Deceleration of an object?
The Deceleration of an object can be calculated through the following formula:
Deceleration (a)= (Final Velocity - initial Velocity)/ total time taken
The unit of Deceleration is the same as Acceleration (metre per second square or “m/s²”). For problems involving the action of gravity, the value of one of the velocities will be 9.8m/s²
3. Give some examples of Deceleration
Various examples of Deceleration can be self noticed in our day to day lives. Some of them are as follows:
A primary example is the use of brakes in a vehicle while in Motion. The vehicle gradually comes to rest, as it decelerates and the Velocity gradually reaches zero.
Similarly when an object is tossed in air, it’s Velocity first increases from zero to its peak. It then quickly decelerates and the Velocity becomes zero at its highest distance from the earth (from where it is tossed).
Airplanes that screech on the runway before coming to rest during landing, also have a very high Deceleration to come to a quick halt.
4. Why is Velocity known as a Vector quantity?
Velocity unlike mass is a Vector quantity. This is because Velocity has both value/ magnitude as well as direction. When a quantity is represented in Vector form it gives information both about its magnitude as well as the direction in which it is working (for example Velocity of an object). And since Velocity is expressed in Vector form, its addition, subtraction and multiplication follow the laws of Vector addition. Velocity (like other Vector quantities in Physics) can be broken down to two components; one along the X-axis and another along the Y-axis.
5. What is the relation between the Deceleration of an object and the Force applied on it?
From Newton’s Second law of Motion, we know that Force (F):
F= mass * Acceleration
Here, it tells us that Force is proportional to the Acceleration of an object. Similarly, when an object decelerates, due to direct proportionality, the Force on the object increases but in the opposite direction, causing the object to halt.
