Position-Time, Velocity-Time and Acceleration-Time Graph

Criteria

P-T Graph

V-T Graph

A-T Graph

X and Y axis

Time and Position

Time and Velocity

Time and Acceleration

Slope

It represents velocity of an object

It represents acceleration of an object.

It represents the jerk or push of a moving object.

Straight slope

Uniform velocity

Uniform acceleration

Uniform jerk

Curvy Slope

Change in velocity

Change in acceleration

Change in the amount of push/jerk



     

       

Average Velocity and Average Speed

Criteria

Average Velocity

Average Speed

Definition 

Change in position or displacement divided by time interval.

Total path length travelled divided by total time interval regardless of direction.

Formula

 

Avg speed = Total path length/Total time interval

Scalar or Vector

Vector

Scalar

Sign

Can be positive or negative

Always positive

Unit

m/s

m/s

 

Instantaneous Velocity and Instantaneous Speed

Instantaneous velocity describes how fast an object is moving at different instants of time in a given time interval. It is also defined as average velocity for an infinitely small time interval.

Here lim is taking operation of taking limit with time tending towards 0 or infinitely small.

dx/dt is differential coefficient – Rate of change of position with respect to time at an instant.

Instantaneous speed is the magnitude of velocity. Instantaneous speed at an instant is equal to the magnitude of the instantaneous velocity at that instant.


Acceleration

Acceleration is rate of change of velocity with time. It is denoted by ‘a’ and the SI unit is m/s2.

Average acceleration is change of velocity over a time interval.


Here v1 and v2 are instantaneous velocities at time t1 and t2.

  • Acceleration can be positive (increasing velocity) or negative (decreasing velocity).
  • Instantaneous acceleration is acceleration at different instants of time. Acceleration at an instant is slope of tangent to the v-t curve at that instant.

  • For a velocity v0 at time t=0, the velocity v at time t will be, v = v0 + a Area under v-t curve represents displacement over given time interval.

  • Acceleration and velocity cannot change values abruptly. The changes are continuous.