NEET Important Chapter - Motion in a Straight Line

Name of the Concept

Key Points of the Concepts

1. State of rest

• Object is said to be at a state of rest when it does not change its position with respect to the time.

2. State of Motion 

• The body or object is said to be in a state of motion with respect to the other body if it changes its position with respect to the time.

3. Rectilinear or linear Motion

• When a body or object moves in such a way that it covers  only  linear distance then it is said to be a linear motion or translational motion. And it is also known as one dimensional motion.

• Under this motion, Only one coordinate in the position is changed.

• Ex. A ball falling freely under gravity.

4. Distance or Path length

• The distance is the total length of actual path traversed by the particle or a body in a definite interval of time.

• distance is a Scalar quantity.

• Its SI unit is meter.

• It depends on the path, not on the final or initial positions of the particle.

5. Displacement

• Displacement is the minimum distance between the initial and final position of a particle in a given interval of time.

•  It is a vector quantity.

•  Its SI unit is meter.

6. Speed

• Speed is the rate of change of distance which is covered by the  body or a particle with respect to time.

• Speed can be classified as uniform and nonuniform.

• Speed is a Scalar quantity

• It’s SI unit is m/s

• Uniform Speed - when a particle covers equal distances in equal intervals of time then it is said to be moving with uniform speed.
  
  

• Non Uniform Speed - In non uniform speed particles cover unequal distances in equal intervals of time or distance traveled by a particle is different in equal interval of time.

• Average Speed - the average speed of a particle for a given interval of time is defined as the ratio of total distance traveled to a total time taken.

• Instantaneous Speed - it is the speed of a particle at a particular instant of time.

7. Velocity

• Velocity  is defined as the rate of displacement of a moving particle with respect to time.

• It is a vector quantity.

• Its SI unit is meters per second.

• Velocity can be classified as uniform and nonuniform velocity.

• Velocity may be positive, negative or zero.

• Uniform Velocity - a particle is set to have a uniform velocity if magnitude as well as direction of its velocity remains same. This is possible only when it moves in the straight line without reversing its direction.

• Non Uniform Velocity - A particle is said to have non uniform velocity if both either magnitude or direction of velocity changes.

• Average Velocity - it is defined as the ratio of displacement to time taken by a particle and its direction is along the displacement.

8. Acceleration

• The rate of change of velocity of an object is called acceleration of the object.

• It is a vector quantity.

• It's direction is same as that of change in velocity (not in the direction of the velocity)

• Its unit is $\dfrac{m}{s^2}$

• Uniform Acceleration - A body said to have uniform acceleration if magnitude and direction of the acceleration remains constant during motion of the particle.

• Non Uniform Acceleration -  A body said to have non uniform acceleration if either magnitude or direction or both change during the motion.

• Average Acceleration - it is the ratio of total change in velocity to the total taken time by the particle or a body.

• Instantaneous Acceleration -  it is the acceleration of a particle at a particular instant of time.

9. Free fall or Motion under gravity

• In the absence of air it is found that all bodies fall with the same acceleration near the surface of earth this motion of body falling towards the earth is called motion under gravity or free fall in free for acceleration of body is equal to acceleration due to gravity

10. Acceleration due to gravity

• Acceleration produced in a body by a force of gravity is called acceleration due to gravity. It is denoted by g.

• Value of g = 9.8 $\dfrac{m}{s^2}$

S.No.

Name of the Concept

Formula

Displacement

$\triangle\overrightarrow{x} = \overrightarrow{x}_2 - \overrightarrow{x}_1$

Average velocity

$\overrightarrow{v}=\dfrac{\triangle \overrightarrow{x}}{\triangle t}$

Instantaneous velocity

$\overrightarrow{v}=\lim_{{\triangle t} \rightarrow 0}\dfrac{\triangle x}{\triangle t} =\dfrac{d\overrightarrow{x}}{dt}$

4.

Average acceleration

$\overrightarrow{a}=\dfrac{\triangle v}{\triangle t}$

5.

Instantaneous acceleration

$\overrightarrow{a}=\lim_{{\triangle t} \rightarrow 0}\dfrac{\triangle v}{\triangle t} =\dfrac{d\overrightarrow{v}}{dt}$

6. 

First equation of motion

$v = u +at$

Here u is initial velocity, v is a final velocity, a is acceleration and t is a time taken.

7.

Second equation of motion

$S = ut + \frac{1}{2} at^2$

Here s is displacement of body, u is initial velocity, v is a final velocity, a is acceleration and t is a time taken.

8.

Third equation of motion

$v^2 =u^2 + 2as$

Here s is displacement of body, u is initial velocity, v is a final velocity and a is acceleration of a body.

9. 

Displacement in nth second

$S_n = ut + \frac{a}{2} (2n - 1)$

10

Maximum height attained by a particle which is projected vertically upward with an initial velocity u

$H = \dfrac{u^2}{2g}$