Deceleration Formula

Deceleration is defined as the rate of change in speed as the body moves away from its initial point. It is also known as negative acceleration as it decreases the velocity of the body to zero. It is the ratio of the difference between the final velocity and initial velocity to the total time taken. It is denoted by the symbol -a. Its unit of measurement is m/s² and the dimensional formula is given by [M⁰L¹T^-2]. Its value must be negative as the velocity of the object is decreasing.

Deceleration Formula

a = -u / t

Where,

• a is the deceleration value
• u is the initial velocity
• t is the total time taken

If the value of distance travelled by the object is given instead of time taken, the formula is given by

a = -u² / 2s

Where,

• u is the initial velocity
• s is the distance covered

Derivation

The deceleration formula is derived by using the first equation of motion.

Suppose an object travels a distance d with an initial velocity of u and negative acceleration of a in a time of t seconds.

So, its final velocity is given by,

v = u + at

We know that the final velocity in this case is zero as the object is decelerating. So, the above equation becomes,

u + at = 0

Solving for a we get,

at = -u

a = -u / t

Similarly the formula can be derived in the terms of distance and time by using the third equation of motion.

v² – u² = 2as

Putting v = 0 we get,

-u² = 2as

a = -u² / 2s

This derives the formula for deceleration.

Sample Questions

Question 1: Calculate the deceleration value if the initial velocity is 10 m/s for a time of 2 s.

Solution:

We have,

u = 10

t = 2

Using the formula we have,

a = -u/t

= -10/2

= -5 m/s²

Question 2: Calculate the deceleration value if the initial velocity is 30 m/s for a time of 5 s.

Solution:

We have,

u = 30

t = 5

Using the formula we have,

a = -u/t

= -30/5

= -6 m/s²

Question 3: Calculate the initial velocity if the deceleration value is 13 m/s² for a time of 6 s.

Solution:

We have,

a = -13

t = 6

Using the formula we have,

a = -u/t

=> -13 = -u/6

=> -u = -78

=> u = 78 m/s

Question 4: Calculate the time taken if the deceleration value is 50 m/s² for an initial velocity of 20 m/s.

Solution:

We have,

a = -50

u = 20

Using the formula we have,

a = -u/t

=> -50 = -20/t

=> 50 = 20/t

=> t = 20/50

=> t = 0.4 s

Question 5: Calculate the deceleration value if the final velocity is 6 m/s for a distance of 5 m.

Solution:

We have,

u = 6

s = 5

Using the formula we have,

a = -u²/2s

= -6²/10

= -36/10

= -3.6 m/s²

Question 6: Calculate the initial velocity if the deceleration value is 15 m/s² for a distance of 20 m.

Solution:

We have,

a = -15

s = 5

Using the formula we have,

a = -u²/2s

=> -15 = -u²/10

=> u² = 150

=> u = 12.24 m/s

Question 7: Calculate the distance traveled if the deceleration value is 4 m/s² for an initial velocity is 30 m/s.

Solution:

We have,

a = -4

u = 30

Using the formula we have,

a = -u²/2s

=> s = -30²/-8

=> s = -900/-8

=> s = 112.5 m