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All questions of Graphs of Motion for EmSAT Achieve Exam

Two stones of different masses are thrown vertically upward with same initial velocity. Which one will rise to a greater height ?
  • a)
    Stone of lower mass
  • b)
    Stone of higher mass
  • c)
    Both will rise to the same height
  • d)
    Information given is insufficient
Correct answer is option 'C'. Can you explain this answer?

Sushil Kumar answered
If we write the equation of motion for both the masses and derive a simple equation to find the maximum vertical height let say H, we get for any particle for some mass m,
H = v2 / 2a
Where a is gravitational acceleration and v is vertical speed. Thus as H does not depend upon m, we get both particles would have equal maximum height.

A ball is thrown vertically upward. At the highest point in its path, which of the following statements is correct?
  • a)
    The velocity is zero and the acceleration is pointing down
  • b)
    The velocity and acceleration are both zero
  • c)
    The acceleration is zero and the velocity is pointing up
  • d)
    The acceleration is zero and the velocity is pointing down
Correct answer is option 'A'. Can you explain this answer?

Geetika Shah answered
Until and unless the velocity of any object comes to zero, any peek in its displacement-time graph can’t be achieved. Which means for the height to be maximised the velocity must become zero. And any time of this motion the acceleration is always a constant downward due to gravity.

In a distance-time graph, if the line is horizontal, then the object is:
  • a)
    Accelerating
  • b)
    Speeding up
  • c)
    At rest
  • d)
    Slowing down
Correct answer is option 'C'. Can you explain this answer?

Destroyed answered
When an object is at rest it will not be able to cover any distance . So for any object at rest the distance -time graph is horizontal to time axis

The area enclosed by velocity-time graph and the time axis will be equal to the magnitude of
  • a)
    displacement
  • b)
    speed
  • c)
    acceleration
  • d)
    distance
Correct answer is option 'A'. Can you explain this answer?

Ishaan Chauhan answered
Explanation:
When an object is in motion, its velocity changes with time. The velocity-time graph shows the variation of velocity with time. The area enclosed by the velocity-time graph and the time axis represents the distance travelled by the object in a given time interval.


Derivation:
Let's consider an object moving with a variable velocity v(t) in a straight line. The velocity of the object at any instant t is given by:

v(t) = ds/dt

where s is the displacement of the object at time t. Integrating both sides, we get:

s = ∫v(t) dt

The integral of velocity with respect to time gives the displacement of the object. The area under the velocity-time graph represents the area of the region bounded by the graph, the time axis and the two vertical lines drawn at the beginning and end of the time interval.


Conclusion:
Therefore, the area enclosed by the velocity-time graph and the time axis represents the displacement of the object. Hence, option 'A' is the correct answer.

The slope of the distance-time graph is:
  • a)
    Distance
  • b)
    acceleration
  • c)
    Speed
  • d)
    Displacement
Correct answer is option 'C'. Can you explain this answer?

Sarita Reddy answered
The gradient of a distance-time graph represents the speed of an object. The velocity of an object is its speed in a particular direction. The slope on a velocity-time graph represents the acceleration of an object. The distance travelled is equal to the area under a velocity-time graph.

For a body performing motion with uniform speed, the distance-time graph is:
  • a)
    Straight line parallel to y-axis
  • b)
    Straight line inclined to the time axis
  • c)
    Straight line parallel to x-axis
  • d)
    Curved line
Correct answer is 'B'. Can you explain this answer?

Rohit Sharma answered
For a body moving at uniform speed, the distance time graph is a straight line inclined to the time axis, which may pass through origin or some other point on the y- axis.

As in uniform motion, the distance time graph would be a straight line, because the equal distance is covered in equal units of time. 

The kinematic equation of motion v = u+at is not applicable if :
  • a)
    Displacement is not constant
  • b)
    motion is non-uniform.
  • c)
    acceleration is not constant
  • d)
    velocity is not constant
Correct answer is option 'C'. Can you explain this answer?

Yash Ghoshal answered
Explanation:

The kinematic equation of motion v = u + at is one of the four equations of motion which are used to describe the motion of an object under constant acceleration. The equation shows the relationship between the initial velocity (u), acceleration (a), time (t), and final velocity (v) of an object. However, this equation is not applicable if the acceleration is not constant.

Constant acceleration means that the rate of change of velocity is constant. If the acceleration is not constant, then the rate of change of velocity is changing, and the equation v = u + at does not hold true for the entire motion.

For example, if an object is moving in a circular path, its acceleration changes direction at every point, and hence, the acceleration is not constant. In this case, the kinematic equation cannot be used to describe the motion of the object.

Similarly, if an object is thrown vertically upwards, the acceleration of the object changes as it moves upwards and then downwards due to the force of gravity. Hence, the kinematic equation v = u + at cannot be used to describe the entire motion of the object.

Conclusion:

In conclusion, the kinematic equation of motion v = u + at is not applicable if the acceleration is not constant, and the rate of change of velocity is changing. The equation is valid only for objects that are moving under constant acceleration. Hence, before using this equation to solve any problem, it is important to check whether the acceleration is constant or not.

What is the slope of distance-time graph when object is at rest?
  • a)
    Decreases continuously
  • b)
    Zero
  • c)
    Increases continuously
  • d)
    One
Correct answer is option 'B'. Can you explain this answer?

Preetam Pyare answered
Since The Body is at Rest ,It clearly means that The Body hasn't covered any Distance here.So,Distance is equal to zero.So,There is no meaning of having any slope here.. So,The Slope=0 Becoz The Distance at anytime will represent same point in Distance-Time Graph at 0..So,(B)is d correct answer. .

 Which of the following quantity does not remain constant during the uniform circular motion?
  • a)
    linear momentum
  • b)
    speed
  • c)
    angular velocity
  • d)
    angular  acceleration
Correct answer is option 'A'. Can you explain this answer?

Geetika Shah answered
  1. Linear momentum is not constant but angular momentum is
  2. Speed has to be constant for “uniform” circular motion
  3. For obvious reasons ω is constant
  4. And the same goes for α

The area under a velocity-time graph is represented by the unit:
  • a)
    m
  • b)
    m-1
  • c)
    m3
  • d)
    m2
Correct answer is option 'A'. Can you explain this answer?

Jyoti Kapoor answered
The area under the velocity-time graph gives the distance (magnitude of displacement) which has the unit: metre (m)


In a velocity-time graph, which variable is plotted on the Y-axis?
  • a)
    Velocity
  • b)
    Speed
  • c)
    Time
  • d)
    Distance
Correct answer is option 'A'. Can you explain this answer?

EduRev Class 9 answered
- In a velocity-time graph:
- The Y-axis represents Velocity.
- The X-axis represents Time.
- Thus, the variable plotted on the Y-axis is Velocity.

The angular velocity (in rad/s) of a body rotating at N r.p.m. is
  • a)
    π N/60
  • b)
    2 π N/60
  • c)
    π N/120
  • d)
    π N/180
Correct answer is option 'B'. Can you explain this answer?

Shreya Gupta answered
Angular velocity is defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω (omega).
Mathematically, angular velocity,
ω =dθ/dt
If a body is rotating at the rate of N r.p.m. (revolutions per minute), then its angular velocity,
ω = 2πΝ / 60 rad/s

On the distance-time graph, the Y-axis should be labeled as:
  • a)
    Distance
  • b)
    Displacement
  • c)
    Speed
  • d)
    Time
Correct answer is option 'A'. Can you explain this answer?

Let's Tute answered
Independent variables are plotted along X-axis and Dependent variables are plotted along Y-axis. In the distance-time graph, time is independent and distance is a dependent variables. Y-axis is Distance
Topic in NCERT: DISTANCE-TIME GRAPHS
Line in NCERT: "In this graph, time is taken along the x-axis and distance is taken along the y-axis."

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