Uniform motion and non-uniform motion

• A body has a uniform motion if it travels equal distances in equal interval of time.
• The distance time graph for uniform motion is a straight line.

• A body has a non-uniform motion if it does not travel equal distance in equal intervals of time. The motion of a freely falling body is an example of non-uniform motion.
• The distance time graph for a non-uniform motion is a curved line.
• A non uniform motion is also called an accelerated or retarded motion.

Speed:

• It is the distance covered in unit time.

• Where v is the speed of the body S is the distance travelled in time t.
• Speed is a scalar quantity as it has only magnitude, but has no specified direction.
• SI unit of speed is m/s or ms^–1.

Uniform speed:

• When a particle covers equal distances in equal intervals of time, then it is said to be moving with uniform speed.
• For example, in illustration given below, motorcyclist travels equal distance (= 5 m) in each second. So we can say that particle is moving with uniform speed of 5 m/s.

Non-uniform (variable) speed:

• In non-uniform speed particle covers unequal distances in equal intervals of time.
• For Example, in illustration given below, motorcyclist travels 5m in 1^st second, 8m in 2^nd second, 10m in 3^rd second, 4m in 4^th second etc. Therefore its speed is different for every time interval of one second. This means particle is moving with variable speed.

Average speed:

• It is the ratio of the total distance travelled (path length) by the object to the total time taken.

          Average speed =

• The average speed of a particle for a given ‘interval of time’ is defined as the ratio of distance traveled to the time taken.

Average speed =

1. Time average speed

• When particle moves with different uniform speed etc in different time intervals t_­1, t_­2, t_­3, ... etc respectively, its average speed over the total time of journey is given as

If time intervals are equal then t₁ = t₂ = t₃ ... t_n = t

• It means average speed is equal to arithmetic mean
• When particle moves with speed v₁ up to half time of its total motion and in rest time it is moving with speed v₂ then

2. When a particle describes different distances d₁, d₂, d₃,... with different time intervals t_­1, t_­2, t_­3, ...  with speeds v₁, v₂, v₃ ... respectively then the speed of particle averaged over the total distance can be given as

• When particle moves the first half of a distance at a speed of v₁ and second half of the distance at speed v₂ then