# Uniform and Non-uniform Motion

Suppose an object moves 10 m in first 10 seconds, 10 m in second 10 seconds, 10 m in third 10seconds, then the motion of the object is uniform motion . Whereas, if the object moves different distances in same time intervals, the motion of the object is non-uniform. Suppose there are two objects A and B whose motion is as shown in the table below –

It is clear that motion of object A is uniform whereas motion of object B is non-uniform.

### Measuring the rate of motion

**1. Speed **

*It is the distance traveled by the object in unit time interval.*- The unit is ms
^{-1}. It is a scalar quantity.

- For uniform motion, the speed does not change over the time.
- But in nonuniform motion the speed changes over the time.
- Average speed is the total distance covered divided by the total time interval.

**2. Velocity**

**Velocity is the speed with direction. In other words, it is the displacement of the object in unit time****interval.**- It is a vector quantity.
- Its unit is same as speed i.e. ms
^{-1}. - For uniform and linear motion, the velocity does not change over the time.
- But, for non-uniform motion, the velocity changes over the time. Here, u = initial velocity and v = final velocity
**The velocity in circular motion changes because the speed does not change but the direction of motion changes . As the speed is not changing on the circular motion, therefore the motion is uniform motion.**

**# Example –** Under what condition is the magnitude of average velocity of an object equal to its average speed?

**Solution** – Average velocity is the ratio of total displacement and total time. If the total displacement is

equal to the total distance covered by the object, then the magnitude of average velocity of the object is equal to its average speed.

**Example –** A boy travels as shown along a straight line for 100 m in 12.5 sec. Then he returns in 12.5 sec. What is his speed and velocity?

Displacement = 100 – 100 = 0 m

Therefore, velocity is zero in this case.

*** Example –** A car travels 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h. Find its average speed.

**Solution –** For first 30 km time is to be calculated from the formula of speed.

Here, speed = 40 km/h and distance = 30km

So,

Time = distance / speed = 30 / 40 = 3 / 4 hrs

For next 30 km, time = distance / speed = 30 / 20 = 3 / 2 hrs

We know,

Now, total time = 3/4 + 3/2 = = 9 / 4 hrs

or Average speed = (30 + 30) / (4/9) = 60 x 4/9 = 240 / 9 = 26.6 km/hr

Therefore, the average speed of the car is 26.6 km/hour.

**# Example –** During an experiment a signal from a spaceship reached the ground station in five minutes.

How far is the spaceship? ( Speed of light is 3 x 10^{8} m/s).

**Solution –**

Distance = Speed x Time

Here,

Speed = 3 x 10^{8} m/s

Time = 300 s

Distance = (3 x 10^{8} ) x 300 = 9 x 10^{10} m

**3. Acceleration or Rate of change of Velocity**

When velocity of a body is increasing, it is said to be accelerating. Suppose a car is at rest and it accelerates to 10 m/s in 10 seconds, then, the rate of change of velocity is 10 / 10 = 1 m/s². Here, 1 m/s² is acceleration of the body.

Thus, **acceleration is defined as the rate of change of velocity of a body with time.**

Here a is acceleration of the body . The SI unit of acceleration is ms^{-2}.

- When a vehicle starts from rest and catches speed, it is accelerating. The acceleration is in the direction of motion.
- When vehicle is moving and brakes are applied, it is retardation. The acceleration is opposite to the direction of motion.
- If the velocity increases at a uniform rate, the acceleration is uniform. Example of such a motion is free fall of a body from a height where the body is accelerated towards earth with uniform acceleration.
- When a car is moving on a crowded road, the driver drives sometimes with increasing speed and sometimes with reducing speed. When a body moves with change in velocity at a non-uniform rate, the body is said to have non-uniform acceleration.

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Graphical representation of motion