# How do I solve a numerical problem based on the motion chapter in class 9?

The Chapter Motion for Class 9 Physics, involves topics limited to straight-line motion. One is straight motion with no acceleration and the other is straight motion with constant acceleration.

This article is especially for class 9 students, studying Motion for class 9.

First of all, there are some important terms that the students need to remember,**Wiexi.com**,and these are:

**Di****stance**

It is defined as the length of the path that is described or travelled by an object that is moving in space. Distance is a scalar quantity given by the SI unit meter denoted by m.

**Displacement**

This on the other hand is the shortest distance that exists between the starting point and the ending point that an object travelled in a particular direction. This is a vector quantity, not a scalar as distance and its SI unit is also meter denoted by m.

**Average Speed**

The total distance that is being covered by the object divided by the total time taken to cover the total distance travelled by it is defined by a term called the average speed which is a scalar quantity. The SI unit of average is meter/sec (m/s). If an object covers the same distance at the same time, then the object is considered to have a constant speed.

**Average Velocity**

Another term is the average velocity which is nothing but a ratio between the total displacement covered or travelled by an object and the total time to cover the total displacement. It is a vector quantity. Its SI unit is meter/s. A body possesses uniform velocity if it covers equal distance at the same time in a specified direction.

**Acceleration**

The change of velocity per unit time is defined as acceleration. is a vector quantity. Its SI unit is m/s^{2}. A body is said to have a uniform acceleration if it travels in a straight line with an increase in velocity in an equal interval of time.

**Some important concepts to remember and understand**

- Distance and displacement are not the same, each has its own definition or explanation. Distance is a scalar quantity whereas displacement is a vector. The distance in a roundtrip is never considered a zero whereas the displacement in a round trip is zero. For example, a person walking around a circle starting from point A and ending in point A, its displacement is taken as zero whereas the distance traveled by it is the circumference.

- The speed is calculated over distance whereas the velocity is calculated over displacement.

- The change in velocity per unit time is known as acceleration. An object that moves with a constant speed but changing the direction will have acceleration as the velocity will change.

**There are various ways to solve Motion problems. Here are some effective steps:**

- Always make a point to read the problem statement properly, visualize it, and then try to solve the question
- Make sure to jot down whatever is given in the question and whatever is required to find or proof. Generally, the initial and final values of quantities are given.
- Next check which concepts or formulae are applicable in solving and find out what principles of physics is required for solving the problem.

**Some important formulae are:**

- s= ut
- v=u+at
- s=ut+(1/2)at
^{2} - v
^{2}=u^{2}+2as

where s is displacement, u is the initial velocity, v is the final velocity and t is the time.

After knowing the formulae, carry out all the calculations and solve them.

**Example:** A car that starts from rest has a uniform acceleration of 1 m/s^{2} along a straight line

- Find the distance moved by car in 5 sec?
- At what time, the velocity becomes 20 m/s?
- How much time it will take to cover a distance of 0.8 km?

Solution:

Given: u=0 m/s, a= 1m/s^{2}, t=5s, v=20 m/s

To find: s, t(20),t

We know that,

- s=ut+(1/2)at
^{2}

Substituting the given values in the equation we have,

s=(0)5 +(1/2)1(5)^{2}=12.5 m

- velocity(v)=20 m/s time, t(20)=?

v=u+at

20=0+1t(20)

or t(20)=20 s

- distance(s)=0.8km=800m t=?

s=ut+(1/2)at^{2}

800=(1/2)(1)t^{2}

or t=40 s

The students need to study and practice the numerical on a daily basis and solve as many questions as they can in order to gain confidence in this particular chapter or topic and have a strong foundation about the different concepts. There are many solution books and guide books that can help students in solving problems from this chapter, however, the students must be thorough with all the basic concepts and theories which they can study from the NCERT textbooks which are available both online and offline. Constant practice is needed as by doing this alone, the students can remember whatever they have learned and practice. Students must be sincere and a proper schedule is needed for a smooth study and practicing of problems without confusion.

Do you know the answer of this question: A particle is moving in a circular path of radius r. The displacement after half a circle would be?