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# Distance Traveled Formula in Physics with Aceleration

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Distance Traveled Formula: All of us travel on a daily basis, whether by vehicle or by foot. When we are going to buy our favorite snack or go for an evening walk, we are basically covering some distance. The same distance concept is available in physics where we deal with various aspects of it. The distance covered by the rocket during its journey into space, the distance between the sun and us, the distance between two planets, etc. are some of the important distances that a physics or mathematics lover may encounter. The distance formula is an important concept in physics as well as mathematics which is used to find many crucial distances of the real world. Let us dive deep into this domain and understand this essential topic.

## Distance Traveled Formula

The distance traveled formula is a mathematical expression that is used to calculate the distance traveled by any object. Distance is defined as the path traced by an object in a given time period. It is important to note that there are different formulas for the distance traveled by an object in different scenarios. Calculating the distance an object travels in a specified amount of time can be done using this formula. Physics and mathematics both depend on the idea of distance traveled, which gives us a way to measure how far an object has moved over time. This measurement is essential in a number of disciplines, including physics, engineering, and daily life. Let us have a look at the formula for the distance traveled.

The formula for the the total distance covered by an object is given by:

D = V x T

where, D = total distance traveled

V = velocity at which the object is moving

T = time period

It must be remembered that the above formula is valid only in cases where the velocity with which the object is traveling remains constant during the journey.

## Distance Traveled Formula Example

Let us understand this formula with the help of a diagrammatic example. Consider the following diagram.

From the above figure,

Let there be an object which start walking from point R as shown by one of the vertices of the above triangle.

The object covers a triangular distance by covering the path from Q and P to back at R

Here, the total distance will be A + B + C,

where A, B, and C are distances travelled which is represented by three edges of the triangle.

In terms of velocity, the distance will be given by D = V x T

where V = velocity of the object during the journey

T = time period taken to complete the journey.

## Distance Traveled Formula with Acceleration

As stated earlier, the above equation holds true only if the velocity remains constant throughout the journey. But what if the velocity is changing during the journey. In that case, we use the distance traveled formula with acceleration. We should know that whenever the velocity of a particular object changes, the concept of acceleration comes into play. Acceleration is basically the rate of change of velocity.

The distance formula with acceleration is expressed as:

D = u x t + (at²)/2

where, u = initial velocity of the object

a = acceleration

t = time period

D = distance traveled

## Distance Traveled Formula Velocity

The distance traveled by the object depends on two factors: its velocity and the time period. velocity plays a major role in determining the distance traveled by the object. If the time period is constant, then the velocity of an object becomes directly proportional to the distance covered by it. The distance covered formula modifies if the velocity of an object takes different value at different time intervals. The modified distance traveled formula for such cases is given below:

D = V1T1 + V2T2 + V3T3 + ………………+ VnTn

where, D = total distance covered

V1 = value of velocity during the time period T1

V2 = velocity during the time period T2

and so on

## Distance Traveled Formula Calculus

The formula for the total distance traveled by an object can be represented in the calculus form too. This formula is helpful for students in case the distance is given in planar co-ordinates or as a function of time. Let us have a closer look at the distance traveled formula in calculus.

D =

where, D = total distance traveled

dt = time period

v(t) = velocity in terms of t

m = starting position of the object

n = final position of the object

## Distance Traveled Formula in nth Second

It is often asked to students to calculate the distance traveled by any object in the nth second. The basic distance covered formula can be tweaked to obtain the distance traveled by the object in the nth second. The distance traveled formula in nth second is given by:

D = V + a(n – 1/2)

where, D = distance covered in the nth second

V = initial velocity

a = acceleration

## Distance Traveled Formula for Kids

The distance traveled is associated with motion, as an object cannot travel or cover a distance without being in motion. It is one of the most important chapter in middle school physics. The physics syllabus of the classes 9 to 12 include the simple equation for the distance traveled. The application of force has also been discussed in these classes, which can be easily understood with the concept of acceleration. So one can easily cover the distance traveled formula for middle classes by reading this informative article.

## Distance Traveled Formula Based Solved Questions

Below we have mentioned some of the solved examples related to this topic. These solved questions will help students understand this concept in a better way.

Example 1: If the velocity of an object is given to be 10 meter per second, then find the distance traversed by this object in 16 seconds?

Solution: We have been given that Velocity (V) = 10 m/s

time period (T) = 16 s

Using the distance traveled formula D= V x T

D = 10 x 16

D = 160 m

so, the distance traveled by the object = 160 meter

Example 2: A vehicle that is fully laden moves at a speed of 4 m/s. Determine the vehicle’s total journey time across a 24-kilometer route.

Solution: We have been given,

velocity (V) = 4 m/s

Total distance traveled (D) = 24 kilometer

we have to find the time period (T)

Using the distance traveled formula D= V x T, and putting the given values

24 km = 4 x T

24 x 1000 m = 4 x T

or, T = (24000)/4

T = 6000 seconds

or, T = 100 minutes or 1 hour 40 minutes

Example 3: The distance traveled by an object is 60 Km in 10 hours. Find its velocity.

Solution: As we know, distance traveled = velocity x time

given, distance traveled = 60 km

so, 60 = velocity x 10

velocity = 60/10

Hence, velocity = 6 km/h

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## FAQs

### What is Distance?

The total path covered by an object in a particular time period is known as distance.

### How is velocity related to the distance?

The velocity is directly proportional to the distance covered. That means, if the velocity of the object is increased, the distance covered by it will also increase.

### Can distance take negative values?

No, the value of distance can never be negative.

### What is the SI unit of distance?

The si unit of distance is meter (m).

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