Search IntMath
Close

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

# Determining Velocity with Time and Change in Acceleration

By Kathleen Cantor, 30 Sep 2020

Every object experiencing an acceleration must have a velocity. This is explained by a branch of physics which is called dynamics. It's an aspect of physics where you study the motion of an object and the forces acting on them.

We can't talk about velocity without talking about speed. By definition, speed is the rate of change of distance with time, while the instrument used to measure the velocity of a moving object is called a speedometer. It measures in kilometer per hour, miles per hour, or feet per hour.

## Determining Velocity With Time And Change In Acceleration

In physics, speed and velocity are often used intermittently. And it is easy to convert from speed to velocity. The unit of speed is kilometer per hour (km/hr.), while that of velocity is meters per second (m/s).

To convert from speed to velocity, you can use the formula below

(Km/hr. x 1000)/ (60 x 60) = m/s

For example, to convert 36 km/hr. to m/s

(36 x 1000)/ (60 x 60) = 10 m/s

### Types of Speed

• Constant/ Uniform Speed: If the rate of change of distance with time is constant throughout a journey, the speed is said to be uniform or constant.
• Average Speed: The average speed is the ratio of the total distance traveled to the total time taken throughout a journey.

Essentially, the average speed is (total distance travelled)/ (total time taken). For example, if a car covers 150 km in 2 hrs, the average speed is (150)/ (2) = 75 km/hr.

### Types of Velocity

Velocity can be defined as the rate of change of displacement with time. Therefore, velocity = (displacement)/ (time) = m/s

• Initial Velocity: This is the velocity of an object before there was an increased acceleration or change in velocity, and it is denoted with U.
• Final Velocity: This is the velocity of an object after there was an increased acceleration or change in velocity, and it is denoted with V.

#### Uniform Velocity

If the rate of change of displacement with time is constant throughout a journey, the body is said to be moving with a uniform velocity.

The change in velocity the velocity of an object is simply the final velocity minus the initial velocity. This change in velocity is also known as acceleration. For example, Change in Velocity = Final Velocity – Initial Velocity

### Acceleration

Acceleration is the rate of change of velocity with time. When an object increases its velocity with time, it's said to accelerate. Therefore, acceleration (a) = (Velocity)/ (Time) = (Change in Velocity)/ (Change in Time) = m/s2

#### Uniform Acceleration

If the rate of change of velocity with time is constant, the acceleration is said to be uniform. If an object’s velocity is decreased, then the acceleration of the object will also decrease with time. When the velocity of an object decreases with time, the process is called deceleration, retardation, or negative acceleration.

#### Example 1

Calculate the acceleration of a train which travels at 36 km/hr and accelerates uniformly to 108 km/hr in 10 sec.

##### Solution
• The initial velocity = (36 x 1000)/ (60 x 60) = 10 m/s
• Final Velocity = (108 x 100)/ (60 x 60) = 30 m/s
• Acceleration (a) = (change in velocity)/ (change in Time) = (30 – 10)/ (10 – 0) = 2 m/s

#### Example 2

A car starting from rest is uniformly accelerated so that its velocity in 5 sec. is 36 km/hr. A break is then applied for it to stop in 4 sec. Find (a) the acceleration (b) the retardation.

##### Solution
• Since the car is starting from rest, the initial velocity (u) = 0
• The final velocity (v) = 36 km/hr. = (36 x 1000)/ (60 x 60) = 10 m/s, time (t) = 5 sec.
• The acceleration (a) = (Final velocity – Initial velocity)/ (change in Time)
• Therefore, (a) = (10 – 0)/ (5 – 0) = 2 m/s
• The retardation = negative acceleration, v = 0 (since the car has come to a stop), u = 10 m/s, t = 4sec.
• Therefore, (a) = (0 – 10)/ (4 – 0) = -10/4 = -2.5 m/s2

### Change In Acceleration

According to Newton’s second law which states that when a force acts on an object, it causes the object to accelerate (change the object’s velocity) at a constant rate. It means that when a force is applied to an object at rest, it will cause it to move in the direction of the force. But if the object is already in motion, it will speed up, slow down or change the direction of movement of the object.

From Newton’s second law

F = Ma, where F = force acting on the object, M= mass of the object, and a= acceleration caused by force.

If you make ‘a’ to be the subject of the formula, then a = F/M

Therefore, if we have a situation in which an object of mass (M) is under the influence of a force ‘F’ with an acceleration (a). If the force is increased, then there will be a positive change in acceleration (a), but if the force is decreased, there will be a negative change in acceleration.

As a result, change in acceleration = (F2 – F1)/M

#### Sample 3

If an object of mass 5 kg is acted upon by a force of 50N to make it move at a velocity of 5 m/s. Find the change in acceleration of the object if the force is increased to 150N.

##### Solution
• F = Ma, F1 = 50N, F2 = 150N, M = 5kg
• Change in acceleration (a) = (150 – 50)/ (5) = 100/5 = 20 m/s2

## Wrapping Up

Calculating the change in velocity with time and change in acceleration of an object is not as hard as you think. You just need to apply the knowledge you have gained from this topic. Make sure that all the variables are in their standard units.

Be the first to comment below.

### Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
a^2 = sqrt(b^2 + c^2)
(See more on ASCIIMath syntax); or
2. Use simple LaTeX in the following format. Surround your math with $$ and $$.
$$\int g dx = \sqrt{\frac{a}{b}}$$
(This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.

From Math Blogs