Question

The speed of a particle changes from $\sqrt{5} \,ms^{- 1}$ to $2 \sqrt{5} \; ms^{-1}$ in a time If the magnitude of change in its velocity is $5 \; ms^{-1}$, the angle between the initial and final velocities of the particle is

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $90^{\circ}$

Answer 1

The Correct Option is D

Given, $v_{i}=\sqrt{5} ms ^{-1}, v_{f}=2 \sqrt{5} ms ^{-1}$ and $\Delta v=5 \,ms ^{-1}$ Since, both $v_{i}$ and $v_{f}$ are extreme speeds, i.e. at $t=0$ and $t=t$. So, they can be considered as magnitude of the velocities at time, $t=0$ and $t=t$. As we know that $R^{2}=A^{2}+B^{2}+2 A B\, \cos\, \theta$ Hence, the angle between the velocities, $\cos \,\theta=\frac{\Delta v^{2}-v_{i}^{2}-v_{f}^{2}}{2 v_{i} v_{f}}$ Putting the given values, we get $ \cos\, \theta=\frac{(5)^{2}-(\sqrt{5})^{2}-(2 \sqrt{5})^{2}}{2(\sqrt{5})(\sqrt{5})} $ $\Rightarrow \cos\, \theta=\frac{25-5-20}{10}$ $=\frac{0}{10}=0 $ $\Rightarrow \theta=90^{\circ}$

Answer 2

Ans. Motion of a body is defined as its change in position over time in response to its environment. Distance, displacement, speed, velocity, acceleration, and time can all be used to measure motion in physics for any object with mass. Based on its velocity, a body's motion can either be uniform or non-uniform. The distance a body has travelled in a unit of time is referred to as the speed of the body in motion, and the displacement in a unit of time is referred to as the velocity. 

Translation describes movement along a line or a curve.

Rotation is the term for motion that alters a body's orientation. 

All motions have a frame of reference in which they are measured.

Linear Motion

Particles move from one point to another in a straight line or a curved path in linear motion. On the basis of the path, the motion can be classified as follows – 

Rectilinear Motion – Motion in a straight line.

Curvilinear Motion – Motion in a curved path.

Examples of linear motion – the motion of the train, the motion of a car on the road, etc.

Rotatory Motion

The motion when a body rotates on its own axis is known as rotatory motion.  

Rotatory motion examples – 

The motion of the earth around the sun about its own axis 

The motion of wheels on their own axis

Oscillatory Motion

The motion of a body about its mean position is known as oscillatory motion. A few examples of  oscillatory motion are

A swing moves to and fro about its mean position.

The pendulum of a clock oscillates as it moves to and fro about its mean position.

The string of the guitar moves to and fro when strummed by its mean position resulting in an oscillatory motion.