Acceleration formula

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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 = (v_f – v_i)/t, where a represents acceleration, v_f is the final velocity, v_i 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.

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

Applying the formula:

• a = (v_f – v_i)/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, v_i = 5 m/s
• Final velocity of an athlete, v_f = 25 m/s
• Time taken by an athlete, t = 5 s
• Acceleration of an athlete, a = ?

Applying the formula:

• a = (v_f – v_i)/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, v_i = 35 m/s
• Final velocity of a bike, v_f = 0 m/s
• Time taken by a bike, t = 7 s
• Deceleration of a bike, a = ?

Applying the formula:

• a = (v_f – v_i)/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, v_i = 12 m/s
• Final velocity of a truck, v_f = 24 m/s
• Time taken by a truck, t = 4 s
• Acceleration of a truck, a = ?

Applying the formula:

• a = (v_f – v_i)/t
• a = (24 – 12)/4
• a = 12/4
• a = 3 m/s²

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

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Related

• Acceleration examples

More topics

• Free fall equation
• Air resistance formula
• Terminal velocity equation
• Gravity equation
• Inertia formula
• Acceleration formula
• Momentum equation
• Mass formula
• Velocity formula
• Pressure equation
• Kinematic equations
• Friction equation

External links

• Acceleration (video) – Khan Academy
• Acceleration Calculator | Definition | Formula – Omni Calculator
• How to Calculate Acceleration: The 3 Formulas You Need – PrepScholar
• 4 Ways to Calculate Acceleration – wikiHow
• Lesson Explainer: Acceleration over Distance and Time – Nagwa
• Acceleration – Wikipedia
• Acceleration Calculator – Symbolab
• Equations of Motion – Isaac Physics
• How to Calculate Acceleration – Physics – Dummies
• Calculating Acceleration from Force and Mass – CK-12
• Acceleration | Definition, Formula & Examples – Study.com
• 3.2 Representing Acceleration with Equations and Graphs – OpenStax
• Acceleration – The Physics Classroom
• Lesson 11: The Other Formulas – Studyphysics
• Angular Acceleration | Physics – Lumen Learning
• Equations of Motion – The Physics Hypertextbook
• 3.3 Average and Instantaneous Acceleration – UCF Pressbooks
• Acceleration – Physics for Kids – Ducksters
• Acceleration vs. Velocity Equations – The Engineering ToolBox
• 3.5: Motion with Constant Acceleration (Part 1) – Physics LibreTexts
• Acceleration: Definition, Formula & Units – Vaia
• Acceleration – National 5 Physics Revision – BBC
• Acceleration – Maths Is Fun
• How to Find Acceleration: Review and Examples – Albert
• acceleration formula – Wolfram Alpha
• Acceleration Calculator – Calculator-online.net