Kinematics MCQ: Solutions & Explanation

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.

Answer: Option c) Distance

Explanation: Distance is a scalar quantity as it has only magnitude and no direction.

Answer: a) Acceleration

Explanation: Acceleration is defined as the rate of change of velocity. It measures the change in velocity per unit of time.

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.

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.

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.

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.

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

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.

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.

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

v_max = (12 x 2) – (3 x 2²) = 12 m/s

Read More: Angular Speed Formula

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).

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.

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.

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.