# How To Find Acceleration With Velocity And Distance: Problem Examples

We all know that distance, velocity, and acceleration are all physical entities that are inextricably linked. As a result, we are going to discuss how to find acceleration with velocity and distance in this post.

When the acceleration is constant in kinematics, the constant acceleration equation can be used to find the acceleration even if you don’t know the time. It can be found by using the initial velocity, the final velocity, and the distance traveled by the object or body.

Before going through how to find acceleration with velocity and distance, let’s go over some constant acceleration equations that can help us find acceleration.

Kinematics is a discipline of physics that deals with the fundamentals of motion. You can find that one precise quantity if a few quantities are known. Constant acceleration equations, also known as kinematics formulae, are a type of problem in which acceleration is calculated using a variety of variables such as distance, velocity, and time. Three equations can be used to determine the acceleration of an object or body in the constant acceleration equation of motion.

## The Constant Acceleration Equations OR The Kinematics Formulas:

Kinematics formulas that are only relevant when an object or body moves with a constant acceleration within a given time interval are known as constant acceleration equations. When it comes to constant acceleration, the acceleration caused by gravity is the best real world example. It is commonly symbolized by the letter ‘g,’ whose value on the earth’s surface is 9.8 m/s2.

The kinematic formulas, often known as constant acceleration equations, are a series of formulas that link the five kinematic variables given below.

• a     Constant Acceleration
• v0   Initial Velocity
• v     Finale Velocity
• t      Time Interval
• 𝛥x   Distance traveled by an object in one direction

Suppose an object or body is under constant acceleration, and three of these five kinematic variables (a, v, v0, t, x) are known. In that case, we can use the kinematic equations given below to solve one of the unknown variables.

1. v = v0 + at

2. 𝛥x = v0t + (1/2)at2

3. v2 = v02 + 2a𝛥x

## How do you choose and apply a constant acceleration formula?

In kinematics, we have three equations of constant acceleration. Out of five kinematic variables, four are present in each equation.

We must select the constant acceleration equation that incorporates both the unknown variable we are looking for and three of the known kinematic variables. By introducing known variable values into the equation, we can find the unknown variable that is only unknown in the equation.

Consider the case of dragging a box that was initially steady. After 5 seconds, its velocity had increased to 10 m/s. Consider a constant acceleration for 5 seconds. Because we have v0, v, and t, we can find the value of the unknown constant acceleration by applying the equation v = v0 + at.

## How to find acceleration with velocity and distance?

The constant acceleration equation is the one that is used in kinematics to find acceleration using velocity and distance.

If we have an initial velocity, a final velocity, and a distance but don’t know the time interval, we can apply the constant acceleration equation  v2 = v02 + 2a𝛥x to get the acceleration.

We have three known quantities and one unknown quantity in the above equation. We can calculate the constant acceleration by placing all three known values in an equation and making acceleration the subject of the equation. As a result, acceleration is determined by rearranging the above equation and given by:

We can find acceleration with velocity and distance using the equation above. Keep in mind that the constant acceleration equations only work if the acceleration is constant (as the name suggests) and in one direction. When dealing with two-dimensional or three-dimensional motion, things become more complicated. However, by applying the above equations for constant acceleration, one may build equations of motion for each direction separately. These simple equations aren’t used when acceleration is changing; instead, complex calculus is used.

Let us see some problems of finding acceleration using velocity and distance.

## Problem: A bike constantly accelerates from rest to a speed of 10 m/s across a distance of 20 m. Determine the acceleration of the bike.

Given:

The initial velocity of the bike v0 = 0 m/s (As initially, the bike is at rest)

Finale velocity of the bike v = 10 m/s

Distance traveled by the bike 𝛥x = 20 m

To Find:

Constant acceleration of the bike a = ?

Solution:

Putting the values in the above equation:

∴ a = 2.5 m/s2

As a result, the bike’s acceleration is 2.5 m/s2.

## Problem: From a height of 1.40 meters, a feather is dropped onto the moon. If the feather’s velocity is 2.135 m/s, then determine the acceleration of gravity on the moon.

Image Credits:  Wikipedia

Given:

Initial velocity of the feather v0 = 0 m/s (As in free falling initial velocity is zero)

Finale velocity of the feather v = 2.135 m/s

Distance traveled by the feather 𝛥x = 1.40 m

To Find:

Acceleration due to gravity on the surface of the moon a = ?

Solution:

Putting the values in the above equation:

∴ a = 1.625 m/s2

As a result, we get the constant value of gravitational acceleration on the moon’s surface, which is 1.625 m/s2.

## Problem: At a speed of 12 m/s, a racing boat crosses the finish line and continues straight ahead. It came to a halt 18 meters from the finish line. What is the magnitude of the acceleration of the racing boat if it instantly decelerates till it comes to a stop?

Given:

Initial velocity of the racing boat v0 = 12 m/s

Finale velocity of the racing boat v = 0 m/s (As it comes to a stop)

Distance traveled by the racing boat 𝛥x = 18 m

To find:

Constant acceleration of the racing boat a = ?

Solution:

Putting the values in the above equation:

∴ a = -4 m/s2

The negative sign indicates that the racing boat’s acceleration decreases and its value is 4 m/s2.

We hope we have answered all of your questions on how to find acceleration with velocity and distance.