The states of motion and rest are relative. Explain? | Physics

MOTION IN A STRAIGHT LINE

Very Short Question Answers

Q1. The states of motion and rest are relative. Explain?
Ans.

Rest: If there is no change in the position of the body with respect to time and its surroundings, then the body is said to be in rest.
Motion: If there is some change in the position of the body with respect to either time or its surroundings, then the body is said to be in motion.
Example: The driver of a moving bus is at rest with respect to a person sitting inside the bus and is in motion with respect to a person outside the bus. Therefore, motion and rest are
relative.

Q2. How is average velocity different from instantaneous velocity?
Ans.

Average velocity: The ratio between total displacement to the total time is called average velocity.

$$ Average \:Velocity =\frac{Total \:displcement}{Total \:time}=\frac{\bigtriangleup x}{\bigtriangleup t}$$

Instantaneous velocity: The velocity of particle at any instant of time is called instantaneous velocity.

$$ Instantaneous \:Velocity= \frac{\mathrm{d}x }{\mathrm{d} t}$$

Q3. Give an example where the velocity of an object is zero but its acceleration is not zero?
Ans.

Vertically projected object at maximum height.
Simple pendulum at any extreme position

Q4. A vehicle travels half the distance L with speed V1 and the other half with speed V2.What is the average speed?
Ans.

$ Average \:speed =\frac{Total \:distance}{Total \:time}$

$\bar{v}=\frac{L}{\frac{\frac{L}{2}}{V_{1}}+\frac{\frac{L}{2}}{V_{2}}}$

$\bar{v}=\frac{2V_{1}V_{2}}{V_{1}+V_{2}}$

Q5. A lift coming down is just about to reach the ground floor. Taking the ground floor as origin and positive direction upwards for all quantities, which one of the following is correct?a) x < 0, v < 0, a > 0 b) x > 0, v < 0, a < 0 c) x > 0, v < 0, a > 0 d) x > 0, V > 0, a > 0
Ans.

a) x<0, v<0, a>0

Q6. A uniformly moving cricket ball is hit with a bat for a very short time and is turned back. Show the variation of its acceleration with time taking the acceleration in the backward direction as positive?
Ans.

MOTION IN A STRAIGHT LINE

Q7. Give an example of one-dimensional motion where a particle moving along the positive X-direction comes to rest periodically and moves forward?
Ans.

A particle in simple harmonic motion comes to rest periodically at the extreme positions

Q8. An object falling through a fluid is observed to have an acceleration given by a= g-bv where g is the gravitational acceleration and b is a constant. After a long time it is observed to fall with a constant velocity. What would be the value of this constant velocity?
Ans.

If velocity is constant, acceleration is zero.

$$a=g-bV$$

$$0=g-bV$$

$$\therefore \:\:V=\frac{g}{b}$$

Q9. If the trajectory of a body is parabolic in one frame, can it be parabolic in a other frame that moves with a constant velocity with respect to the first frame? If not, what can it be?
Ans.

No, it can be a straight line

Q10. A spring with one end attached to a mass and the other to a rigid support is stretched and released. When is the magnitude of accele ation a maximum?
Ans.

At extreme positions acceleration of mass is maximum.

Short Question Answers

Q1. Can the equations of kinematics be used when the acceleration varies with time? If not,what form would these equations take?

Ans. No.But,the equations of kinematics can be used even when the acceleration varies with time.

Inteqration form
$$\int _{v_0}^v dv= \int _0^t adt$$

$$\int_{x_0}^xdx= \int_0^t\left(v_0+at\right)dt$$

Q2. A particle moves in a straight line with uniform acceleration. Its velocity at time t = 0 is V? and at time t = t is V? . The average velocity of the particle in this time interval is (V? +V?)/2. Is this correct? Substantiate your answer?