Initial Velocity Formula, Definition, Solved Example

Initial Velocity Formula: Initial Velocity, denoted as u, signifies the velocity at time interval t = 0, representing the velocity at the beginning of motion. There exist four formulas to calculate initial velocity:

When time (t), acceleration (a), and final velocity (v) are given, the initial velocity (u) is expressed as:

Initial Velocity Formula u=v−at

In the case of given values for final velocity (v), acceleration (a), and distance (s), the formula is:

Initial Velocity Formula  u ² =v ² −2as

If the provided values are distance (s), acceleration (a), and time (t), the formula for initial velocity is:

Initial Velocity Formula u=  s/t ​ −  1/2 ​ at

Where: Initial velocity is represented as  u Final velocity is denoted as  v Time taken is  t Distance traveled or displacement is  s Acceleration is  a In the scenario where final velocity (v), distance (s), and time (t) are given, the formula for initial velocity is:

Initial Velocity Formula u=  2(s/t )​ −v

Initial Velocity Formula Solved Examples

Example 1: A car accelerates from rest at a rate of 4 m/s² for a duration of 5 seconds. Calculate the final velocity of the car.

Answer: Given: Initial velocity  u = 0 m/s (as the car starts from rest) Acceleration  a = 4 m/s² Time  t = 5 s

Using the Initial Velocity Formula v=u+at

v=0+(4×5)

v=20m/s

Therefore, the final velocity  v is 20 m/s.

Example 2: An object is thrown vertically upward with an initial velocity of 15 m/s. If the acceleration due to gravity is 9.8 m/s 2 9.8m/s 2 , find the time it takes for the object to reach its highest point.

Answer: Given: Initial velocity u = 15 m/s Acceleration  a (due to gravity) = −9.8m/s ² (negative because it acts downward) Using the formula v=u+at, and knowing that at the highest point v=0

0=15−9.8t

Solving for t= 15/9.8 ​

t≈1.53s

Therefore, it takes approximately 1.53 seconds for the object to reach its highest point.

Example 3: A ball is dropped from a height of 25 meters. Determine the final velocity just before it hits the ground. Take the acceleration due to gravity as 9.8m/s ² .

Answer: Given: Initial velocity  u = 0 m/s (ball is dropped, so initial velocity is zero) Acceleration  a (due to gravity) = 9.8m/s ² Distance  s (height) = 25 m

Using the formula v ² =u ² +2as

v ² =0+2×9.8×25

v ² =2×9.8×25

v ² =490

Taking the square root to find v ² = 490 ​

v≈22.14m/s Therefore, the final velocity just before the ball hits the ground is approximately 22.14m/s.

Example 4: A car decelerates from a speed of 30 m/s to rest in 5 seconds. Calculate the acceleration and the distance traveled during the deceleration.

Answer: Given: Initial velocity u = 30 m/s Final velocity  v = 0 m/s (as the car comes to rest) Time t = 5 s

Using the formula a= v−u / t​ to find acceleration: a= 0−30/5 ​

a=−6m/s 2

The negative sign indicates deceleration.

Using the formulas=ut+ 1/2 ​ at 2 to find distance traveled:

s=30×5+ 2 1 ​ ×(−6)×(5 2 )

s=150−75

s=75m

Therefore, the acceleration is −6m/s 2 (deceleration), and the distance traveled during the deceleration is 75 meters.

Example 5: A car accelerates from rest at a rate of 3 m/s² for a duration of 5 seconds. Calculate the final velocity of the car.

Answer: Given: Initial velocity  u = 0 m/s (as the car starts from rest) Acceleration  a = 3 m/s² Time  t = 5 s

Using the formula v=u+at

v=0+(3×5)

v=15m/s

Therefore, the final velocity  v is 15 m/s.

Example 6: A car accelerates from rest at a rate of 2 m/s² for a duration of 5 seconds. Calculate the final velocity of the car.

Answer: Given: Initial velocity  u = 0 m/s (as the car starts from rest) Acceleration  a = 2 m/s² Time  t = 5 s

Using the formula v=u+at

v=0+(2×5)

v=10m/s

Therefore, the final velocity  v is 10 m/s.

Example 7: A car accelerates from rest at a rate of 8 m/s² for a duration of 5 seconds. Calculate the final velocity of the car.

Answer: Given: Initial velocity  u = 0 m/s (as the car starts from rest) Acceleration  a = 8 m/s² Time  t = 5 s

Using the formula v=u+at

v=0+(8×5)

v=40m/s

Therefore, the final velocity  v is 40 m/s.

Explore Now Online Course of Class 9 Neev Fastrack 2024 and Class 10 Udaan Fastrack 2024 to enhance your Physics knowledge. and build a strong foundation.