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Kinematics. JUNIOR EAMCET. Distance and Displacement. B. 5m. 3m. A. O. 4m. O to B: distance is 7m and displacement is 5m. Distance and Displacement. B. C. 5m. 3m. A. O. 4m. O to C along OABC: distance is 11m and displacement is 3m. Distance and Displacement. B. C. 5m. 3m. A.

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Kinematics

Kinematics

JUNIOR EAMCET


Distance and displacement
Distance and Displacement

B

5m

3m

A

O

4m

O to B: distance is 7m and displacement is 5m


Distance and displacement1
Distance and Displacement

B

C

5m

3m

A

O

4m

O to C along OABC: distance is 11m and displacement is 3m


Distance and displacement2
Distance and Displacement

B

C

5m

3m

A

O

4m

O to O along OABCO: distance is 14m and displacement is zero


Arc of a circle
Arc of a Circle

B

A

R

R

Arc length AB is R

AB jaw length is


Average speed and average velocity
Average Speed and Average Velocity

v

u

t

t

u

v

s

s

Both averge speed and average velocity


Average speed and average velocity1
Average Speed and Average Velocity

u

s

v

s

Both averge speed

Both averge velocity


Train crossing a bridge
Train Crossing a Bridge

u

Time of crossing the post is

s

Train

Post

u

Time of crossing the bridge is

L

s

Train

Bridge


Average speed and averge velocity
Average Speed and Averge Velocity

Average speed =

u

B

A

Average velocity =

R

u

Average acceleration =


Direction of acceleration
Direction of Acceleration

Acceleration is positive if v > u

a

u

v

Direction of acceleration is v – u

Acceleration is negative if v < u

u

v

a


Sign application
Sign Application

Downward direction is positive

+ g

Freely falling body

S, u, v, g, h are all positive

Upward direction is positive

Body projecte up

a = – g

u, v, h are all positive


Body projected from the top of a tower
Body Projected From the Top of a Tower

Upward direction is positive

u

a = – g

u is positive

s, g are negative

s = – h


Tossing in a train
Tossing in a Train

If Vt = Vb : a = 0; the ball falls in the hand

If Vt > Vb : a > 0 the ball falls bedhind

If Vt < Vb : a < 0; the ball falls in front


Vn – Vn-1 = a

Vn = u + an

Vn-1 = u + a(n – 1)

Sn – Sn-1 = a


t

Displacement = average velocity × time

v

u

s

If u = 0


a

A travels with acceleration a, B with uniform velocity u

A

u

If they start simultaneously

B

Time of meet is

u

a

d

A

If A is ahead of B

B

u

If B is ahead of A

a

d

A

B


One body projected and the other falling freely
One Body Projected and the Other Falling Freely

Time of meet is

u = 0

h

Height of meet is

u = u

h = h1 + h2


Time taken to reach the ground is t1 when throuwn up

Time taken to reach the ground is t2 when thrown down

t1

u

u

t2

h

Time of free fall is

Initial velocity u =

Height h =


Water drops from the tap
Water Drops from the Tap

(n – 1)t =

‘t’ is time interval with which the drops are released

h

Ratio of displacements of 4th, 3rd, 2nd and 1st drops is 1 : 3 : 5 : 7


h height of the window

u velocity at the top of the window

t time of crossing the window


If the velocity is reduced by after travelling a distnce x, then the total distance it can travel is


If th front and back of the train cross a post with velocities u and v, the center will cross the same post with velocity ----

u

x

v


Graphical representation
Graphical Representation velocities u and v, the center will cross the same post with velocity ----

v

Uniform velocity

10m/s

a

-a

9

O

t

7

3

5

a

-5


Graphical representation1
Graphical Representation velocities u and v, the center will cross the same post with velocity ----

v

Uniform velocity

10m/s

-5

10/3

20

15

10

9

O

-5

t

7

3

5

a

-5


Graphical representation2
Graphical Representation velocities u and v, the center will cross the same post with velocity ----

v

vmax

O

t


V t graph
V – t Graph velocities u and v, the center will cross the same post with velocity ----

The slope gives acceleration

Acceleration is positive if  < 90

v

Acceleration is negative if  > 90

P

Area represents displacement

O

Displacement is positive if area is above x - axis

t


Graphical representation3
Graphical Representation velocities u and v, the center will cross the same post with velocity ----

v

a

u constant

u

u = 0

-a

a

O

t


u velocities u and v, the center will cross the same post with velocity ----

s

A

B

Distance is 2s

Displacement is zero

v

Time for forward journey is

Average speed is

Time for return journey is


u velocities u and v, the center will cross the same post with velocity ----

t

a

u

t

a

d


Equations of motion
Equations of Motion velocities u and v, the center will cross the same post with velocity ----

X = a + bt + ct2


Problem
Problem velocities u and v, the center will cross the same post with velocity ----

Find the acceleration


Problem1
Problem velocities u and v, the center will cross the same post with velocity ----


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