# Distance Traveled Formula

## Distance Traveled Formula

In their daily lives, all humans travel to some locations. Additionally, they cover a certain amount of miles during their journey. However, from the scientific perspective, distance is a measurement type that takes a variety of elements into account. Furthermore, students will learn about the Distance Traveled Formula with examples in the course of their studies. Students can learn the idea of the Distance Traveled Formula in simple terms.

The notes and solutions for the Distance Traveled Formula are also made available in Hindi for students of various other boards. Comprehension of the Distance Traveled Formula is made easier with the help of these notes, owing to Extramarks’ subject matter experts. The notes and solutions based on the Distance Traveled Formula have been prepared in accordance with the CBSE syllabus emulating the structure of the NCERT books.

### Total Distance Traveled Formula

Students only need to integrate the velocity function to determine the displacement (position shift) from it. The entire displacement was removed from the negative regions below the x-axis. Then students need to apply a displacement formula in the nth second to this.

Displacement is equal to ba a b v (t) dt.

They must utilise the absolute value in order to determine the Distance Traveled Formula.

Sn = u + a(n 1/2) gives the displacement in the nth second Distance Traveled Formula that is covered in the nth second.

### Uses and Applications of Distance Traveled Formula

The Distance Traveled Formula can be used for calculating and determining how far driving a car or swimming laps in a pool will take one. Driving a car will involve calculating distance in miles or kilometres, speed in miles per hour or kilometres per hour, and time in hours. The distance will be computed in laps while swimming laps in a pool.

### Displacement in nth Second Formula

Science says that

= displacement

t = Time

Initial Velocity = u

accelerating with a

Continuing with the solution:

u = An object’s initial velocity

accelerating with a

Sn is the distance travelled in n seconds from a place that is crucial.

When the second equation of motion is calculated,

figuring out how far something has travelled in t seconds

S = ut + ½ at2

figuring out how far something has travelled in n seconds

Un + 1/2an2 = Sn

Currently, the distance travelled in the next (n – 1) seconds

Sn-1 = u (n – 1) + 1/2 a (n-1)

2

measuring the distance nth seconds travelled

Snth = Sn-S (n-1),

Snth is equal to un + 12 an2 – [u(n-1) + 12 a(n-1)2].

When the aforementioned equation is condensed,

Snth = u + a/1/2 (2n-1).

Sn = u + a (n – ½).

Consequently, the equation for the distance travelled in an nth second is

Sn = u + a (n – ½).

Students can find a detailed description of the Distance Traveled Formula on the Extramarks website and mobile application.

### Derive the Expression for the Formula for Displacement in the nth Second

The term “Distance Traveled Formula” describes how far an object has travelled during a specified amount of time to get to its destination. The path that a body takes to travel a specific distance at a certain speed from one location to another is known as the Distance Traveled Formula. Additionally, by seeing this in formula form, it can be understood in a more meaningful way. The calculation of the Distance Traveled Formula is provided.

𝑑=𝑟×𝑡

The formula for calculating distance travelled can be used to calculate how far driving a car or swimming laps in a pool will take one. The distance and speed while driving an automobile are measured in kilometres and kilometres per hour, respectively. The distance swum will be measured in terms of laps while doing laps in a pool.

### Solved Examples

Example 1: A loaded truck moves at a speed of 60 kilometres per hour. Determine how long it will take the truck to travel 200 kilometres in total.

Solution: Considering the parameters,

r, or the travel speed, is 60 km/h.

Distance, d, equals 200 kilometres

We also understand that

d=rt Displacement

The time required will be provided as follows:

𝑡=𝑑𝑟

=20060

= 3.33 hours

Time is therefore 3.33 hours.

Example 2: An athlete can run 50 metres in 10 seconds while another athlete can run 200 metres in 30 seconds. Who is moving more quickly?

Solution: First athlete’s displacement is 50 metres, and the time required is 10 seconds.

His speed will therefore follow the formula.

𝑟1=5010

r1 is equal to 10 m/s.

The first participant moved 200 metres and took 30 seconds.

His speed will therefore follow the formula.

𝑟2=20030

r2 is equal to 6.67 m/s.

The second athlete has therefore moved more quicker.

## FAQs (Frequently Asked Questions)

### 1. What is the Distance Travelled in the Last Second Formula?

The body’s initial velocity is 0 mph.

using v=u+at

One discovers v=0+an.

t=2 for displacement over the previous two seconds.

Considering that S= vt2a t2.

also S=v (2) nv (2)

2

S= 2v – 8nv

S= 2v(1-22n) (1-22n)

### 2. Where can students access the Distance Traveled Formula?

Students can access the notes for the Distance Traveled Formula on the Extramarks website and mobile application.