# Science: Motion and Its Description: Average Speed and Acceleration (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Average Speed

The average speed can be determined by the ratio of total distance covered to the total time taken.

Similarly, in case of average velocity in place of total distance covered you can take total displacement.

Position-time Graph To draw graph of the motion of an object, its position at different times are shown on y-axis and time on x-axis. For example, positions of an object at different times are given.

Time (s) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Position (m) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

## Acceleration

This change in velocity with time is called acceleration. Thus, the acceleration of an object is defined as the change in velocity divided by the time interval during which this occurs.

Its unit is ms^{-2}. It is specified by direction. Its direction is along the direction of change in velocity. Suppose the velocity of an object changes from 10 ms ^{– 1} to 30 ms ^{– 1} in a time interval of 2 s.

- If the acceleration of an object during its motion is constant, we say that object is moving with uniform acceleration.
- When velocity of the object is constant, acceleration will be zero. Thus, for uniform motion, the acceleration is zero and for non-uniform motion, the acceleration is non-zero.

## Equation of Motions

Consider an object moving with uniform acceleration, *a*. Let *u* be the initial velocity (at time *t* = 0) , *v*, velocity after time *t* and *S*, displacement during this time interval. There are certain relationships between these quantities.

This is called as the first equation of motion.

Also, we know that,

This is called the second equation of motion.

If object starts from rest, *u* = 0 and

Thus, we see that the displacement of an object undergoing a constant acceleration is proportional to t^{2}, while the displacement of an object with constant velocity (zero acceleration) is proportional to t.