**Motion**

**"Change of position with time"**

Distance Vs Displacement

Distance or Displacement?

Distance = ................

Displacement = ..................

Distance Vs Displacement

Distance

Displacement

Exercise

Q1: A man travels 20 m to the north; then turns east and travels 30m after which he again turns north and covers another 20m. What is the Distance he covered? What was his displacement?

Exercise

Q2: A person moved along the following path from point A to B; point B to C and then point C to A.

What is the Distance Traveled?

What is the Displacement?

Uniform & Non-Uniform Motion

A body traveling equal distance in equal time intervals (no matter how small or large these intervals are)

Example????

Uniform Motion

Non Uniform Motion

Unequal distance in equal time intervals

Uniform Motion

Non Uniform Motion

Example????

Speed

Distance travelled per unit time

Speed =

Distance

Time

Average Speed

Average Speed =

Total Distance Traveled

Total Time Taken

DO NOT confuse this with “Uniform Speed”

Exercise

Q3: A cyclist covers a distance of 5 KM in 15 minutes. What is his speed in:

- Kilometer per hour

- Meter per second

Exercise

Q4: Vikas drives 180KM in 3 hrs while Vipin drives 150KM in 2.5 hrs. Who drives faster?

Exercise

Q5: A car travels first 5 km at 20km/h and the next 5 km at 30 km/h. What is its average speed?

Exercise

Q6: On a 120 km track, a train travels the first 30 km at a uniform speed of 30 km/h. How fast must the train travel the next 90 km so as to average 60 km/h for the entire trip?

Units???

Unit ???

**Distance & Displacement**

**Uniform & Non-uniform**

Motion

Motion

**Speed**

**Velocity**

**Velocity =**

**Distance Traveled in a given direction**

**Time Taken**

**Distance traveled per unit time in a given direction**

**Velocity =**

**Displacement**

**Time Taken**

or

**Unit???**

Uniform Velocity

If a body travels in a specific direction in straight line and moves over equal distances in equal intervals of time

The velocity fo the body can be changed by:

1. by changing the speed of the body, and

2. by changing the direction

Exercise

Q. Usha swims in a 90 m long pool. She covers 270 m in one minute by swimming back and forth from one end to the other along the same straight path. Find the average speed and average velocity of Usha.

Exercise

Q. A bus covers a distance of 250 km from Delhi to Chandigarh towards north in 4 hrs in the morning. In the evening it returns back to Delhi in 6 hrs. Find the average speed and average velocity for the whole journey.

**Acceleration**

Acceleration =

Change in velocity

Time Taken for change

**Rate of change of velocity in unit time**

Acceleration =

Final velocity - Initial velocity

Time taken

=

**v - u**

**t**

**Unit???**

Uniform Acceleration

Velocity increases or decreases by equal amounts in equal intervals of time

Examples???

Retardation /Deceleration / Negative Acceleration

If the velocity of the body decreases, the acceleration in negative.

final velocity < initial velocity

Retardation is acceleration with a negative sign

Exercise

Q. Starting from a stationary position, Rahul paddles his bicycle to attain a velocity of 6 m/s in 30 sec. Then he applies brakes such that the velocity of the bicycle comes down to 4 m/s in the next 5 sec. Calculate the acceleration of the bicycle in both the cases.

Exercise

Q. A train starting from a railway station and moving with uniform acceleration attains a speed 40 km/h in 10 minutes. Find its acceleration.

Exercise

Q. A bus decreases its speed from 80 km/h to 60 km/h in 5 sec. Find the acceleration of the bus.

**Equations of Motions**

First Equation of Motion

Second Equation of Motion

Third Equation of Motion

First Equation of Motion

v = u

+

at

v

= final velocity

u

= initial velocity

a

= acceleration

t

= time taken

Second Equation of Motion

s = ut + ½ at

s

= distance travelled

u

= initial velocity

a

= acceleration

t

= time taken

***for uniformly accelerated motion**

2

Third Equation of Motion

v = u + 2as

v

= final velocity

u

= initial velocity

s

= distance traveled

a

= acceleration

2

2

Important Points

1. if a body starts from rest, its initial velocity,

u

= 0

2. if a body comes to rest (it stops), its final velocity,

v

= 0

3. if a body moves with uniform velocity, its acceleration,

a

= 0

Exercise

Q. A train starting from rest attains a velocity of 72 km/h in

5 minutes. Assuming that the acceleration is uniform, find (i) the acceleration and (ii) the distance traveled by the train for attaining this velocity.

Exercise

Q. A car accelerates uniformly from 18 km/h to 36 km/h in 5 sec. Calculate (i) the acceleration and (ii) the distance covered by the car in that time.

Exercise

Q. The brakes applied to a car produce an acceleration of 6 m/s in the opposite direction to the motion. If the car takes 2 s to stop after the application of brakes, calculate the distance it travels during this time.

2

Exercise

Q. A racing car has a uniform acceleration of 4 m/s . What distance will it cover in 10 s after start?

2

Exercise

Q. A trolley, while going down an inclined plane, has an acceleration of 2 cm/s . What will be its velocity 3 s after the start?

2

**Graphical Representation of Motion**

Distance-Time Graph

Speed -Time Graph

Distance-Time Graph

Speed-Time Graph

Depict:

1. Uniform Speed

2. Non-uniform Speed

Calculate: Speed

Depict:

1. Constant Speed

2. Uniform Acceleration

3. Uniform Retardation

4. Non-Uniform Acceleration

Calculate: Distance, Acceleration

Exercise

a. What type of motion is rep. by OA, AB & BC

b. What is the acceleration of body during OA, BC

c. What is the distance traveled by body during OA, AB and BC

Exercise

Q. A car is moving on a straight line with uniform acceleration. The speed of the car at different times is as follows:

Draw a speed time graph by choosing a convenient scale. Determine from it:

1. acceleration of the car

2. the distance covered by the car in 50 sec.

Derive Equation of Motion by Graphical Method

Derive:

1. v = u + at

2. s = ut + 1/2 at

3. v = u + 2as

2

2

2

**Uniform Circular Motion**

An object moving in a circular path with uniform speed, the motion is called uniform circular motion

The motion with constant speed along a circular path is an example of an accelerated motion. Why?

Examples???

Velocity during Circular Motion

v = 2πr / t

v

= velocity

t

= time taken

Exercise

Q. A cyclist goes around a circular track once every 2 minutes. If the radius of the circular track is 105 meters, calculate his speed (π = 22/7)