Identify the unit vector in the following?

(a)

\(\hat { i } +\hat { j } \)

(b)

\(\frac { \hat { i } }{ \sqrt { 2 } } \)

(c)

\(\hat { k } -\frac { \hat { j } }{ \sqrt { 2 } } \)

(d)

\(\frac { \hat { i } +\hat { j } }{ \sqrt { 2 } } \)

If a particle has negative velocity and negative acceleration, its speed

(a)

increases

(b)

decreases

(c)

remains same

(d)

zero

If the velocity is \(\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k } \), then the magnitude of acceleration at t = 0.5s is

(a)

1 ms^-2

(b)

2 ms^-2

(c)

zero

(d)

-1 ms^-2

If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 ms^-2) 

(a)

77.3 m

(b)

78.4 m

(c)

80.5 m

(d)

79.2 m

Which one of the following satatement is true?

(a)

A scalar quantity is conserved in a process

(b)

A scalar quantity does not vary from one point to another in apace

(c)

A scalar quantity can never take -ve values

(d)

A scalar quantity has only magnitude and no direction.

The angle between A i +j and B = i - j is ______________.

(a)

45°

(b)

90°

(c)

-45°

(d)

180°

The component of position vector \(\overrightarrow { r } \) along x-axis will maximum value if ____________

(a)

\(\overrightarrow { r } \) is along the x - axis

(b)

\(\overrightarrow { r } \) makes an angle of 45° with x - axis

(c)

\(\overrightarrow { r } \)  is along the y - axis

(d)

\(\overrightarrow { r } \)  is along - ve y - axis 

Consider the quantities pressure, power, energy, impulse, charge. Out of these, the only vector quantity is _______________.

(a)

pressure

(b)

power

(c)

impulse

(d)

charge

The length of a vector is _______________

(a)

always a negative quantity

(b)

always a positive quantity

(c)

either positive or negative

(d)

denoted by '\(\lambda \)' 

Distance is a scalar quantity and ______________ is a vector.

(a)

Speed

(b)

Length

(c)

Time

(d)

Displacement

Explain what is meant by Cartesian coordinate system?

Define a vector. Give examples.

Define a scalar. Give examples

What is Kinematics?

What is meant by frame of reference?

What is right handed coordinate system?

How do you deduce that two vectors are perpendicular?

Define displacement and distance.

Define velocity and speed

What is meant by point mass and give suitable example?

What do you mean by motion in one, two and three dimensions?

What are the different types of vectors?

Two vectors \(\vec A\) and \(\vec B\) of magnitude 5 units and 7 units respectively make an angle 60° with each other as shown below. Find the magnitude of the resultant vector and its direction with respect to 7 unit the vector \(\vec A\).

Derive the relation between Tangential acceleration and angular acceleration.