- Introduction
- Average velocity
- Instantaneous velocity
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- Average and instantaneous acceleration
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- Motion with constant acceleration
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- Projectile Motion
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- Uniform circular motion
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- Motion in three dimensions

**(A)** A plank of length L is moving in the direction of x-axis in the X-Y plane. A point A is located on the left hand side of the plank. Position of point A at t=0 is (L,0). The plank is moving in the right direction with velocity v

**Question 1**

A person standing at point A at t=0 throws a stone with velocity v and at an angle 60^{0} with X axis. Find the co-ordinates of the maximum height reach by the stone

**Question 2 **

Find the velocity vector at the maximum height if **i** and **j ** are the unit vectors along X and Y axis respectively

**Question 3**

Find the co-ordinates of the stone where its hit the X-axis

**Question 4**

Find the velocity vector of the stone when it hits X-axis.

**Question 5**

Find the co-ordinates of the point A on the plank when the stone hit the X-axis

**Question 6**

Find the maximum value of velocity v so as to land the stone on the plank

**(B)** Two ring X and Y are put on two vertical stationary rods AB and A^{’}B^{’}. An inextensible thread is fixed at point A^{’} and on ring X and is passed through ring Y.

The system is shown below in Figure

**Question 7**

The ring X moves with constant velocity v downwards. The angle AXY is θ. Find the velocity of the ring Y

**Question 8**

Find the velocity of ring Y with respect to ring X

**(C)** A man X can swim at a speed of 10 m/s with respect to river . He wants to cross the river which is 50 m wide and has a current of 5 m/s

If he wishes to land on the other bank at a point directly across the river from his starting point

**Question 9**

Velocity of man with respect to the person standing on the bank

a) 5

b) 10

c) 6

d)5√3

**Question 10**

Find the angle made by the man from the current

a) 120^{0}

b) 60^{0}

c) 30^{0}

d) 90^{0}

**Question 11**

Find the time taken by the man to cross the river

**(D)**Now if he instead decides to cross the river in shortest possible time

**Question 12**

what direction it should swim

a) 90^{0} to current

b) 30^{0} to current

c) 60^{0} to current

d) none of these

**Question 13 **

How much time

a) 5

b) 10

c) 6

d) 4

**Question 14**

How much distance it will land from his starting point

a) 30

b) 20

c) 25

d) none of these

**(E)**The radius vector describing the position of the particle A relative to origin

**Question 15**

Find the rectangular components of the average velocity in the time interval between t and t+?t

**Question 16**

Which of the following statements are true about the motion

a) The particle is experiencing uniform acceleration motion

b) The particle starts at y axis and touched x axis in 1sec

c) The initial velocity is towards negative Y axis

d) The velocity at t=1 is towards positive x axis

**(F)** A particle is moving along a parabola given by

y=x^{2}

So that at any time v_{x}=3 m/s

**Question 17**

Find the magnitude and direction of velocity at x=1/3 m

**Question 18**

Find the acceleration at x=1/3 (both magnitude and direction)

a) 18 m/sec^{2} ,90^{0}

b) 14 m/sec^{2} ,60^{0}

c) 18 m/sec^{2} ,60^{0}

d) 14 m/sec^{2} ,90^{0}

**(G)**An object is fired up on the inclined place of angle α . The object is fired with velocity v_{0} and angle of elevation θ with the horizontal

**Question 19**

Find the range on the inclined plane

**Question 20**

Find the relation between and α for which object will have maximum range

**Answers**

- (c)
- (a)
- (b)
- (b)
- (a)
- (b)
- (a)
- (b)
- (d)
- (a)
- (a)
- (a)
- (a)
- (c)
- (a)
- (a),(b),(c),(d)
- (c)
- (a)
- (b)
- (a)

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