Acceleration

• Let an object moving with an initial velocity 'u' attain a final velocity 'v' in time 't', then acceleration 'a' produced in the object is

(Acceleration = Rate of change of velocity with time)

Unit of acceleration:

The SI unit of velocity is m/s and time is s

(∴ SI unit of acceleration is = m/s²)

(Acceleration is a vector quantity)

Different types of Acceleration:

• Acceleration is of different types depending on the change in velocity.

Positive Acceleration:

• If the velocity of an object increases then the object is said to be moving with positive acceleration.

Example:

• A ball rolling down on an inclined plane.

Negative Acceleration:

• If the velocity of an object decreases then the object is said to be moving with negative acceleration. Negative acceleration is also known as retardation or deceleration.

Example:

1. A ball moving up an inclined plane.

2. A ball thrown vertically upwards is moving with a negative acceleration as the velocity decreases with time.

Uniform Acceleration:

• If the change in velocity in equal intervals of time is always the same, then the object is said to be moving with uniform acceleration.

Example: A body falling from a height towards the surface of the earth.

Non-uniform or Variable Acceleration:

• If the change in velocity in equal intervals of time is not the same, then the object is said to be moving with variable acceleration.

Distance time graph for uniform speed:

• When a body moves with uniform speed, it will travel equal distances in equal intervals of time or we can say the distance travelled by a body is directly proportional to time. The slope of distance time graph shows the speed of the body.
• Graph for uniform speed will be a straight line.
• If a displacement time graph is drawn, then it will represent velocity.

Distance time graph for non-uniform speed:

• If the speed of a body is non-uniform, then the graph between distance travelled and time is a curved line.

Conclusion:

1. If the distance time graph is a straight line then the body is said to be in uniform speed. Similarly if the displacement time graph of a moving body is a straight line, then it represents uniform velocity of the body.
2. If the distance time graph of a body is a curved line, then the body is said to be in non uniform speed.

Speed time graphs:

1. When the speed of a body is constant then there is no acceleration
2. When the speed of the body changes at uniform rate then there is uniform acceleration
3. When the speed of the body changes in a non-uniform way then there is non-uniform acceleration.

Speed time graph when the speed of the body is constant:

• In this case the speed of the body does not change with respect to time and hence there is no acceleration. So speed-time graph for a body moving with constant speed is a straight line parallel to the time axis. In other words we can say that if speed –time graph of a body is a straight line parallel to the time axis, then the speed of the body is constant.
• In this case distance travelled is Area of rectangle

Speed-time graphs when speed changes at uniform and non-uniform rate:

1. Acceleration:

• The Speed- time graph for a uniformly changing speed will be a straight line and slope of the graph will represent acceleration.
• When the speed of a   body changes in an irregular manner, then the speed time graph of the body is a curved line.

2. Decreasing acceleration (deceleration)

Speed-time graph when the initial speed of the body is not zero:

• In this case the distance travelled by the body is equal to the area of trapezium.

Uses of Velocity-time Graphs:

• The following results can be deduced from velocity-time graph.
• The acceleration produced in a body
• The distance covered by a moving object
• We can derive the equations of motion