# Acceleration formula

The acceleration formula describes the relationship between acceleration (a), change in velocity (Δv), and time (t). It states that acceleration is equal to the ratio of the change in velocity to the time taken. Mathematically, the formula for acceleration is given as a = (vf – vi)/t, where a represents acceleration, vf is the final velocity, vi is the initial velocity, and t is the time interval. This formula allows for the calculation of the acceleration of an object based on the given values of velocity change and time.

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## Practice problems

### Problem #1

A car initially at rest accelerates to 24 m/s in 12 s. What is the acceleration of a car?

Solution

Given data:

• Initial velocity of a car, vi = 0 m/s
• Final velocity of a car, vf = 24 m/s
• Time taken by a car, t = 12 s
• Acceleration of a car, a = ?

Applying the formula:

• a = (vf – vi)/t
• a = (24 – 0)/12
• a = 24/12
• a = 2 m/s2

Therefore, the acceleration of a car is 2 m/s2.

### Problem #2

An athlete accelerates from 5 m/s to 25 m/s in 5 s. Calculate the athlete’s acceleration.

Solution

Given data:

• Initial velocity of an athlete, vi = 5 m/s
• Final velocity of an athlete, vf = 25 m/s
• Time taken by an athlete, t = 5 s
• Acceleration of an athlete, a = ?

Applying the formula:

• a = (vf – vi)/t
• a = (25 – 5)/5
• a = 20/5
• a = 4 m/s2

Therefore, the acceleration of an athlete is 4 m/s2.

### Problem #3

A bike traveling at 35 m/s comes to rest in 7 s when the brakes are applied. Calculate the bike’s deceleration.

Solution

Given data:

• Initial velocity of a bike, vi = 35 m/s
• Final velocity of a bike, vf = 0 m/s
• Time taken by a bike, t = 7 s
• Deceleration of a bike, a = ?

Applying the formula:

• a = (vf – vi)/t
• a = (0 – 35)/7
• a = (-35)/7
• a = -5 m/s2

Therefore, the deceleration of a bike is -5 m/s2.

### Problem #4

A truck accelerates from 12 m/s to 24 m/s in 4 s. What is the truck’s acceleration?

Solution

Given data:

• Initial velocity of a truck, vi = 12 m/s
• Final velocity of a truck, vf = 24 m/s
• Time taken by a truck, t = 4 s
• Acceleration of a truck, a = ?

Applying the formula:

• a = (vf – vi)/t
• a = (24 – 12)/4
• a = 12/4
• a = 3 m/s2

Therefore, the acceleration of a truck is 3 m/s2.