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Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. It focuses on describing and analyzing the position, velocity, and acceleration of objects as a function of time.
Examples of kinematic concepts include -
- Displacement: The change in position of an object over a certain period of time
- Velocity: The rate of change of displacement over time
- Acceleration: The rate of change of velocity over time
These concepts can be applied to a wide range of physical systems, such as a ball being thrown, a car moving along a road, or a rocket launching into space. By analyzing the kinematic behavior of these objects, we can understand how they move and how their motion can be affected by various factors such as air resistance, friction, and gravity.
MCQ on Kinematics
Ques 1. What is the definition of kinematics?
a) The study of the motion of objects without considering the cause of motion
b) The study of the motion of objects including the cause of motion
c) The study of the motion of objects in the absence of any force
d) The study of the motion of objects in the presence of any force
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Answer: Option a) The study of the motion of objects without considering the cause of motion
Explanation: Kinematics is the study of the motion of objects without considering the cause of motion. It focuses on describing the motion in terms of position, velocity and acceleration.
Ques 2. Which of the following is a scalar quantity?
a) Velocity
b) Acceleration
c) Distance
d) Force
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Answer: Option c) Distance
Explanation: Distance is a scalar quantity as it has only magnitude and no direction.
Ques 3. The rate of change of velocity is known as
a) Acceleration
b) Speed
c) Momentum
d) Force
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Answer: a) Acceleration
Explanation: Acceleration is defined as the rate of change of velocity. It measures the change in velocity per unit of time.
Ques 4. What is the formula for velocity?
a) Velocity = Displacement/Time
b) Velocity = Time/Displacement
c) Velocity = Displacement x Time
d) Velocity = Displacement - Time
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Answer: a) Velocity = Displacement/Time
Explanation: Velocity is defined as the rate of change of displacement with respect to time. It is calculated as the ratio of displacement of the particle to the time taken.
Ques 5. What is the formula for acceleration?
a) Acceleration = Velocity/Time
b) Acceleration = Time/Velocity
c) Acceleration = Velocity x Time
d) Acceleration = Velocity - Time
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Answer: a) Acceleration = Velocity/Time
Explanation: Acceleration is defined as the rate of change of velocity with respect to time. It is calculated as the ratio of the change in velocity to the change in time.
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Ques 6. What is the formula for displacement?
a) s = ut + 0.5at2
b) s = ut - 0.5at2
b) s = vt - 0.5at2
d) s = vt + 0.5at2
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Answer: a) s = ut + 0.5at2
Explanation: The formula for displacement is s = ut + 0.5at2 where u is the initial velocity, a is the acceleration and t is the time.
Ques 7. What is the formula for final velocity?
a) v = u + at
b) v = u - at
c) v = at - u
d) v = t/u
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Answer: a) v = u + at
Explanation: The formula for final velocity is v = u + at where u is the initial velocity, a is the acceleration and t is the time.
Ques 8. What is the formula for the time taken for an object to reach a certain height under gravity?
a) t = √(2h/g)
b) t = √(h/2g)
c) t = √(2g/h)
d) t = √(g/2h)
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Answer: a) t = √(2h/g)
Explanation: The formula for the time taken for an object to reach a certain height under gravity is t = √(2h/g) where h
Ques 9. What does the area under the acceleration-time graph represent for any given time interval
(a) Final velocity
(b) Distance travelled
(c) Change in the velocity in that time interval
(d) Displacement of the particle
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Answer: c) Change in the velocity in that time interval
Explanation: The area under the acceleration-time graph represents the change in velocity in that time interval.
- Acceleration is the rate of change of velocity, and it can be positive or negative.
- If the acceleration is positive, the velocity of the particle is increasing, and if the acceleration is negative, the velocity of the particle is decreasing.
- The area under the acceleration-time graph during a given time interval is equal to the change in velocity of the particle during that time interval.
- The formula for the change in velocity is given by the equation:
Δv = at
- where Δv is the change in velocity, a is the acceleration, and t is the time interval.
So, the area under the acceleration-time graph during a given time interval represents the change in velocity of the particle during that time interval, and it gives the final velocity of the particle at the end of the time interval.
Therefore, option (c) is the correct answer.
Ques 10. When can we say that the resultant of two vectors is maximum?
a) Both the vectors are acting in opposite directions
b) Both the vectors are acting in the same direction
c) The vectors are perpendicular to each other
d) The vectors are acting at a 45-degree angle to each other
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Answer: b) Both the vectors are acting in the same direction
Explanation: The resultant of two vectors is maximum when they are acting in the same direction.
- This means that their effect is additive, and they combine to produce the maximum force or magnitude.
- On the other hand, when the vectors are acting in opposite directions, their effect is subtractive, and the resultant will be less than the individual vectors.
- When the vectors are perpendicular to each other, their effect is not additive or subtractive, but rather the resultant is at a right angle to both vectors.
- The same is true for vectors acting at a 45-degree angle to each other.
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Ques 11. What is the maximum velocity of a particle that moves in a straight line and its position is defined by the equation x = 6t2 - t3 (where t is in seconds and x is in meters)?
a) 12 m/s
b) 6 m/s
c) 9 m/s
d) 3 m/s
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Answer: a) 12 m/s
Explanation: To find the maximum velocity of the particle, we need to find the derivative of the position equation with respect to time.
dx/dt = 12t - 3t2
But dx/dt = v, velocity of the body
⇒ v = 12t - 3t2 ...(i)
Velocity will be maximum when dv/dt = 0
⇒ dv/dt = d/dt (12t - 3t2) = 0
⇒ dv/dt = 12 – 6t = 0
⇒ t = 2 s
Substituting t = 2 s in equation (i) to get the maximum value of velocity
vmax = (12 x 2) – (3 x 22) = 12 m/s
Read More: Angular Speed Formula
Ques 12. If u1 and u2 are the velocities of two moving bodies in the same direction before impact and v1 and v2 are their velocities after impact, then the coefficient of restitution is given by:
a) (v1 + v2)/(u1 + u2)
b) (v2 - v1)/(u1 + u2)
c) (v2 - v1)/(u1 - u2)
d) (v1 + v2)/(u1 - u2)
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Answer: c) (v2 - v1)/(u1 - u2)
Explanation: The coefficient of restitution (e) is a value that represents the elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of the approach of two bodies before impact. The relative velocity of separation (v2-v1) is divided by the relative velocity of approach (u1-u2) to find the coefficient of restitution. Hence, the correct answer is (v2 - v1)/(u1 - u2).
Ques 13. During elastic impact, the relative velocity of the two bodies after impact is:
a) greater than the relative velocity of the two bodies before impact
b) equal and opposite to the relative velocity of the two bodies before impact
c) the same as the relative velocity of the two bodies before impact
d) less than the relative velocity of the two bodies before impact
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Answer: b) equal and opposite to the relative velocity of the two bodies before impact
Explanation: During an elastic impact, the total momentum of the two bodies before and after impact is conserved. This means that if the relative velocity of the two bodies before impact is given by v, then the relative velocity of the two bodies after impact is equal and opposite to v. The impact is considered elastic if the bodies bounce back after the collision and there is no net loss of energy.
Ques 14. The coefficient of restitution of a perfectly plastic impact is:
a)1
b)0.5
c)0
d)-1
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Answer: c) 0
Explanation: The coefficient of restitution (e) is a measure of the elasticity of a collision, defined as the ratio of the relative speed of separation to the relative speed of approach of two colliding bodies. For a perfectly plastic impact, the two colliding bodies will stick together and the relative speed of separation is 0. Therefore, the coefficient of restitution is 0, indicating a perfectly inelastic collision.
Ques 15. What is impulse equal to?
a) Change in position
b) Change in velocity
c) Change in mass
d) Change in momentum
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Answer: d) Change in momentum
Explanation: Impulse is defined as the product of force and time, and it is a measure of the influence of a force on a body. The SI unit of impulse is the Newton-second (N s). Impulse can also be expressed as the change in the momentum of a body. Momentum is defined as mass times velocity, and when a force acts on a body, it changes its velocity and thus its momentum. Hence, the change in momentum of a body is equal to its impulse.
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