#### IIT (NTSE/Olympiad)

# Motion in one Dimension

__Acceleration __

__Acceleration__

It is defined as the rate of change of velocity.

It is defined as the acceleration of a body at some particular instant.

Instantaneous acceleration =

A body is said to have non-uniform acceleration, if magnitude or direction or both change during motion.

i.e. if is given as a function of time, second time derivative of displacement gives acceleration.

= tan θ

**(i)**It is a vector quantity.**(ii)**Its direction is same as that of change in velocity and not of the velocity (That is why acceleration in circular motion is towards the centre)**(iii)**There are three ways possible in which change in velocity may occurWhen only direction | When only magnitude changes | When both the direction changes and magnitude change |
---|---|---|

To change the direction net acceleration or net force should be perpendicular to direction of velocity Example: Uniform circular motion | In this case, net force or net acceleration should be parallel or anti-parallel to the direction of velocity. (straight line motion)Example: When ball is thrown up under gravity. | In this case, net force or net acceleration has two components. One component is parallel or anti-parallel to velocity and another one is perpendicular to velocity Example : Projectile motion |

**Types of acceleration :****(a) Instantaneous acceleration :**It is defined as the acceleration of a body at some particular instant.

Instantaneous acceleration =

**(b) Average acceleration :****(c) Uniform acceleration :**A body is said to have uniform acceleration if magnitude and direction of the acceleration remains constant during particle motion.**Note :**If a particle is moving with uniform acceleration, this does not necessarily imply that particle is moving in straight line.**Example :**Parabolic motion**(d) Non-uniform acceleration :**A body is said to have non-uniform acceleration, if magnitude or direction or both change during motion.

**Note :****(i)**Acceleration is a vector with dimensions [LT^{–2}] and SI units (m/s^{2})**(ii)**If acceleration is zero, velocity will be constant and motion will be uniform.**(iii)**However if acceleration is constant then acceleration is uniform but motion is non-uniform and if acceleration is not constant then both motion and acceleration are non-uniform.**(iv)**If a force acts on a particle of mass m then by Newton's II law**(v)**As by definitioni.e. if is given as a function of time, second time derivative of displacement gives acceleration.

**(vi)**If velocity is given as function of position then by chain rule**(vii)**As acceleration the slope of velocity-time graph gives acceleration i.e.= tan θ

**(viii)**The slope of -t curve, i.e. is a measure of rate of non-uniformity of acceleration. However we do not define this physical quantity as it is not involved in basic laws or equation of motion.**(ix)**Acceleration can be positive or negative. Positive acceleration means velocity is increasing with time while negative acceleration called retardation means velocity is decreasing with time.#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension
- Distance
- Displacement
- Comperative Study of Distance & Displacement
- Speed
- Velocity
- Comparative Study of Instantaneous Speed and Instantaneous Velocity
- Comparative Study Of Average Speed & Average Velocity
- Acceleration
- Motion With Uniform Acceleration
- Motion Under Gravity
- Relative – Velocity
- Points to Remember - Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS

- GRAVITATION