Question
Figure gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of $v$ and a in the three intervals. What are the accelerations at the points A, B, C and D?
 Image

Answer

(i) We know that the average acceleration in a small time interval is equal to the slope of the (v – t) graph in that time interval.
That is, magnitude of average acceleration
$=\frac{\text { change in speed }}{\text { time interval }}$
The slope of the $(v-t)$ graph is maximum in interval 2 as compared to intervals 1 and 3 . Hence, the magnitude of mean acceleration is maximum in interval 2.
(ii) The average velocity is maximum in interval 3 and minimum in interval 1 because the rise of $D$ on the speed axis is highest.
(iii) V is positive in interval all three intervals i.e., $v>0$. In interval 1 the acceleration is positive, in interval 2 the acceleration is negative and in 3 the acceleration is zero.
(iv) Due to the gradient being positive in time interval 1 and 3, the value of acceleration (a) will be positive, but due to the gradient being negative in time interval 2, the value of acceleration a is also negative i.e., $a >0$ in time intervals 1 and 3. $a>0$ in interval 2.
(v) At points A, B, C and D on velocity-time graph is parallel to the x -axis. For this reason the value of acceleration a will be zero at all these points. (The speed is the same at these four points).

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is 1.50 × 108 km away from the sun ?
In a microwave oven, the food is kept in a plastic container and the microwave is directed towards the food. The food is cooked without melting or igniting the plastic container. Explain.
When a fat person tries to touch his toes, keeping the legs straight, he generally falls. Explain with reference to figure.

Consider the situation shown in figure. The width of each plate is b. The capacitor plates are rigidly clamped in the laboratory and connected to a battery of emf $\in.$ All surfaces are frictionless. Calculate the value of M for which the dielectric slab will stay in equilibrium.

The cylindrical tube of a spray pump has a cross-section of $8.0 cm^2$ one end of which has 40 fine holes each of diameter 1.0 mm . If the liquid flow inside the tube is $1.5 m min ^{-1}$, what is the speed of ejection of the liquid through the holes?
Read the passage given below and answer the following questions from (i) to (v).
Root mean square velocity (RMS value)is the square root of the mean of squares of the velocity of individual gas molecules and the Average velocity is the arithmetic mean of the velocities of different molecules of a gas at a given temperature.

  1. Moon has no atmosphere because:-
    1. It is far away from the surface of the earth
    2. Its surface temperature is 10°C
    3. The r.m.s. velocity of all the gas molecules is more than the escape velocity of the moon’s surface
    4. The escape velocity of the moon’s surface is more than the r.m.s velocity of all molecules
  2. For an ideal gas, CPCV is
    1. >1
    2. <1
    3. ≤1
    4. none of these
  3. The root mean square velocity of hydrogen is 5 times than that of nitrogen. If T is the temperature of the gas then:
    1. T(H2) = T(N2)
    2. T(H2) < T(N2)
    3. T(H2) > T(N2)
    4. none of these
  4. Suppose the temperature of the gas is tripled and N2 molecules dissociate into an atom. Then what will be the rms speed of atom:
    1. v06
    2. v0
    3. v03
    4. none of these
  5. The velocities of the molecules are v, 2v, 3v, 4v & 5v. The rms speed will be:
    1.  11 v
    2.  v(11)12
    3.  v
    4.  v(12)11
Read the passage given below and answer the following questions from 1 to 5.
Newton’s first law of motion states that If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero only if there is a net external force on the body. To summaries, if the net external force is zero, a body at rest continues to remain at rest and a body in motion continues to move with a uniform velocity. This property of the body is called inertia. Inertia means ‘resistance to change’. A body does not change its state of rest or uniform motion, unless an external force compels it to change that state.  In other words, all objects resist a change in their state of motion. In a qualitative way, the tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. Consider a book at rest on a horizontal surface. It is subject to two external forces: the force due to gravity (i.e. its weight W) acting downward and the upward force on the book by the table, the normal force R. R is a self-adjusting force. This is an example of the kind of situation mentioned above. The forces are not quite known fully but the state of motion is known. We observe the book to be at rest. Therefore, we conclude from the first law that the magnitude of R equals that of W. A statement often encountered is : Since W = R, forces cancel and, therefore, the book is at rest”. This is incorrect reasoning. The correct statement is: “Since the book is observed to be at rest, the net external force on it must be zero, according to the first law. This implies that the normal force R must be equal and opposite to the weight W.
  1. The book on table is at rest. The force of gravity here is balanced by:
  1. Force of friction.
  2. Normal reaction by table on book.
  3. Weight of table.
  4. None of these.
  1. If no external force acts on object which is at rest. it will
  1. Remain at rest.
  2. Start to move.
  3. Both a and b can possible.
  4. None of these.
  1. Define inertia.
  1. State Newton’s first law of motion.
  1. Explain why book on table remains at rest.
A spring balance has a scale that reads from 0 to 50 kg . The length of the scale is 20 cm . A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s . What is the weight of the body ?
No part of India is situated on the equator. Is it possible to have a geostationary satellite which always remains over New Delhi?
Read the passage given below and answer the following questions from (i) to (v).
Kelvin-Planck statement: No process is possible whose sole result is the absorption of heat from a reservoir and the complete conversion of the heat into work.
Clausius statement: No process is possible whose sole result is the transfer of heat from a colder object to a hotter object. It can be proved that the two statements above are completely equivalent.
A thermodynamic process is reversible if the process can be turned back such that both the system and the surroundings return to their original states, with no other change anywhere else in the universe. a reversible process is an idealized motion. A process is reversible only if it is quasi-static (system in equilibrium with the surroundings at every stage) and there are no dissipative effects. For example, a quasi-static isothermal expansion of an ideal gas in a cylinder fitted with a frictionless movable piston is a reversible process.
The free expansion of a gas is irreversible. The combustion reaction of a mixture of petrol and air ignited by a spark cannot be reversed. Cooking gas leaking from a gas cylinder in the kitchen diffuses to the entire room. The diffusion process will not spontaneously reverse and bring the gas back to the cylinder. The stirring of a liquid in thermal contact with a reservoir will convert the work done into heat, increasing the internal energy of the reservoir. The process cannot be reversed exactly; otherwise it would amount to conversion of heat entirely into work, violating the Second Law of Thermodynamics. Irreversibility is a rule rather an exception in nature.
  1. The diffusion process is:
  1. Reversible process
  2. Irreversible process
  1. A quasi-static isothermal expansion of an ideal gas in a cylinder fitted with a frictionless movable piston is
  1. Reversible process
  2. Irreversible process
  1. State Kelvin Planck statement.
  2. State Clausius statement.
  3. Define reversible processes and irreversible processes of thermodynamics.