Acceleration MCQ Quiz - Objective Question with Answer for Acceleration - Download Free PDF

Correct option is: (2) −2 / (2x + 1)³

t = x² + x

We have

dt/dx = 2x + 1

⇒ v = dx/dt = 1 / (2x + 1)

⇒ dv/dx = −2 / (2x + 1)²

⇒ a = v × dv/dx = [1 / (2x + 1)] × [−2 / (2x + 1)²]

= −2 / (2x + 1)³

CONCEPT:

Position Vector and Acceleration

• The position vector of a particle provides information about its location in space as a function of time.
• Acceleration is the rate of change of velocity with respect to time.
• To find acceleration, we need to differentiate the position vector twice with respect to time.

EXPLANATION:

• Given position vector: r(t) = 15t² i + (4 - 20t²) j
• First, we find the velocity by differentiating the position vector with respect to time:
  • v(t) = dr(t)/dt = 30t i - 40t j
• Next, we find the acceleration by differentiating the velocity with respect to time:
  • a(t) = dv(t)/dt = 30 i - 40 j
• At t = 1, the acceleration vector is:
  • a(1) = 30 i - 40 j
• To find the magnitude of the acceleration:
  • |a(1)| = √(30² + (-40)²)
  • |a(1)| = √(900 + 1600)
  • |a(1)| = √2500
  • |a(1)| = 50

Therefore, the correct answer is option 4: 50.

First particle moving towards east Initial velocity of particle

After some time velocity towards North velocity of partially

Change in velocity , Time taken .

Average acceleration =

Average acceleration , the direction is north-west

making with X-axis.

Concept Used:

The slope of the velocity-time graph gives the acceleration of the body. If the graph is a straight line, the slope is constant and represents the acceleration. In this case, the angle between the line and the time axis is given as 60°.

Formula Used:

Acceleration (a) = slope of the velocity-time graph = tan(θ)

Calculation:

We have:

⇒ Acceleration (a) = tan(60°)

⇒ tan(60°) = √3

∴ The correct answer is: √3

Concept:

Magnetic Induction and Eddy Currents in a Metal Pipe:

• When a bar magnet is dropped through a hollow metal pipe, it creates a changing magnetic flux as it falls.
• This changing magnetic flux induces eddy currents in the metal pipe due to electromagnetic induction.
• These eddy currents generate their own magnetic field, which opposes the motion of the magnet (Lenz's Law).
• The opposition to the magnet's motion results in a reduced acceleration compared to free fall under gravity.
• Thus, the acceleration of the falling magnet is less than g (acceleration due to gravity).

Calculation:

When a magnet is dropped through the hollow metal pipe, the induced eddy currents create a force that opposes the motion of the magnet.

This results in a reduced net force and consequently, the acceleration of the magnet is less than the gravitational acceleration g.

∴ The acceleration of the falling magnet is less than g. Option 2) is correct.

The correct answer is (v-u)/t.

CONCEPT:

• Acceleration: The rate of change in velocity is called acceleration. It is denoted by a.
  • The SI unit of acceleration is m/s².
• Equation of motion: The mathematical equations used to find the final velocity, displacements, time, etc of a moving object without considering force acting on it are called equations of motion.
• V = u + at
• Where, V = final velocity, u = initial velocity, a = acceleration of body under motion, and t = time taken by the body under motion.

EXPLANATION:

From the above equation of motion:

V = u + a t

So a = (V - u)/t

• The formula for finding acceleration is (v-u) / t. So option 4 is correct.

Additional Information

• The product of velocity and time (v x t) represents the displacement of a body which represents the shortest distance between two points.
• The reciprocal of time (1 / t) represents the frequency of oscillations which gives the value of the total number of oscillations in the given time.
• The work per unit time (W / t) represents power which is the measurement of the rate of doing work.

The correct answer is velocity.

Key Points

• Acceleration is the rate at which velocity changes with respect to time.
• The ultimate outcome of all forces applied to a body, according to Newton's second law, is its acceleration. Acceleration, a vector quantity, determines the frequency at which a body's velocity varies. The formula can be used to express acceleration.
• The overall movement of an object, regardless of direction, is referred to as distance.
• The term "displacement" refers to a shift in an object's position. It's a vector quantity with a magnitude and a direction.
• The product of a particle's mass and velocity is called momentum. Momentum is a vector quantity in the sense that it has both a magnitude and a direction.

CONCEPT:

• Velocity: The rate of change of displacement of a body is called the velocity of that body.
  • Velocity is a vector quantity that has both magnitudes as well as direction.
• Acceleration: The rate of change of velocity is called the acceleration of the body.
  • Acceleration is also a vector quantity.
  • The slope of any velocity-time graph gives an acceleration of the body.
• Displacement: The minimum path length between two points is called displacement.
• Distance: The total path length between two points is called distance.

EXPLANATION:

• The slope of any graph is the ratio of the vertical change between two points to the horizontal change between the same points.
• In a velocity-time graph, the velocity (v) is present on the vertical axis while time (t) on the horizontal axis, so the slope of the graph is given by:

• Since the rate of change of velocity is termed as acceleration, the slope of a velocity-time graph gives the acceleration.
• Therefore the slope of the velocity-time graph for retarded motion is negative. Therefore option 3 is correct.

Additional Information

• Similarly, the slope of displacement - time graph gives velocity.
• The area under the velocity-time graph gives displacement and the area under the acceleration - time graph gives the change in velocity.

The correct answer is option 4) i.e. ​jerk

CONCEPT:

• Acceleration is defined as the rate of change of velocity.
  • The SI unit of acceleration is m/s2.

Acceleration, a = 

Where v is the velocity during the time period t.

• Jerk or jolt is defined as the rate of change of acceleration with respect to time.
  • It is said to occur when an object experiences a sudden pull/push or irregular movement.

EXPLANATION:

• The slope of an acceleration time graph equals the ratio of change in acceleration for the time interval considered.

Slope =  = rate of change of acceleration = jerk

​Additional Information

• Velocity is the rate of change of displacement with time. It is obtained from the slope of the displacement-time graph.
• Impulse is the change in momentum of an object when the object is acted upon by a force for a certain amount of time.
• Force is a push or pull that acts on an object and changes its state of rest/motion or shape or direction.

CONCEPT: 

ACCELERATION & DECELEARATION:

• Acceleration is the measure of the rate of change of velocity with respect to time, the value of acceleration can be both positive and negative.  

​                                                                                                                                                                                                                   Where v= Final velocity, u =Initial velocity and t = time 

•  Deceleration is the negative rate of change of velocity.        

CALCULATION:

Given - x = 8 + 12t - t3

• As we know, velocity is defined as the rate of change of displacement.

When V = 0, then

⇒ 12 - 3t² = 0

⇒ 12 = 3t²

⇒ t = 2 sec

• The retardation is given by

CONCEPT:

• Velocity (v): The rate of change of displacement of a body is called the velocity of that body.
  • Velocity is a vector quantity that has both magnitudes as well as direction.
• Acceleration (a): The rate of change of velocity is called the acceleration of the body.
  • Acceleration is also a vector quantity.
  • The slope of any velocity-time graph gives an acceleration of the body

a = dv/dt

Velocity (v) = dx/dt

Where x is displacement and t is time

• Uniform acceleration: When the acceleration is constant then it is called uniform accelerated motion.
• Non-uniform acceleration: When the acceleration is not constant then the motion is non-uniform accelerated motion.

CALCULATION:

Given that:

v2 = ax²

Differential both sides with respect to x,

2v (dv/dx) = 2ax

Since a = dv/dt, and Velocity (v) = dx/dt

Now 

Hence acceleration (a) = v(dv/dx) = ax

• Since a is constant so acceleration will be a variable that changes with displacement x and hence non-uniform acceleration.

The correct answer is velocity.

Key Points 

CONCEPT:

• Velocity/ speed: The rate of change of displacement/distance of a body is called the velocity/speed of that body.
  • Velocity is a vector quantity that has both magnitudes as well as direction.
• Acceleration: The rate of change of velocity is called the acceleration of the body.
  • Acceleration is also a vector quantity.
• The slope of any velocity-time graph gives an acceleration of the body.
• Displacement: The minimum path length between two points is called displacement.
• Distance: The total path length between two points is called distance.

Explanation:

From the above explanation, we can see that, 

• Acceleration is the rate of change of velocity
• In other words, it is the ratio of change in velocity and time taken
• It has SI units of m/s2 and is also the derivative of velocity

Additional Information

Concept: 

Acceleration:

• It is defined as the rate of change of velocity with respect to time.
• Formula, acceleration,  where, dv = change in velocity, dt = change in time
• The SI unit of acceleration is m/s2.
• It is a vector quantity because it has both magnitude and direction.
• The area under the acceleration - time graph represents the change in velocity.

Calculation:

We know that, 

The area under the acceleration - time graph represents the change in velocity

Hence, the maximum change in velocity is 60m/s.

Additional Information

Velocity:

• It is defined as the rate of change of displacement with respect to time.
• Formula, velocity,  where ds = change in displacement, dt = change in time
• The SI unit of velocity is m/s.
• The area enclosed under the velocity-time graph gives Displacement.

CONCEPT:

• Velocity (v): The rate of change of position i.e. rate of displacement with time is called velocity.
  • It is a vector quantity.
• Speed (v): The rate of change in distance is called speed. It is a scalar quantity.
• Acceleration (a): The rate of change of velocity is called the acceleration of the body.
  • Acceleration is also a vector quantity.
• Momentum (p): The product of mass and velocity is called momentum.
  • It is a vector quantity.

EXPLANATION:

• Acceleration due to gravity: The earth always attracts the body towards its centre and the acceleration due to this force is called acceleration due to gravity.
• It is denoted by g.

g  = 10 m/s² which is constant.

• When a ball is thrown in the air then this acceleration acts on it. Thus the acceleration of the ball remains constant which is equal to g in a downward direction. So option 3 is correct.
• Due to this acceleration, the speed, velocity and momentum of the ball changes with time as the velocity reduce because of retardation due to gravity.

The correct option is 4.

CONCEPT:

• Velocity (v): The rate of change of position i.e. rate of displacement with time is called velocity.

Where s2 = displacement of the object at t2 and s1 = displacement of the object at t1

• It is a vector quantity.

EXPLANATION:

• The slope of any graph is the ratio of the vertical change between two points to the horizontal change between the same points.
• In a velocity-time graph, the velocity (v) is present on the vertical axis while time (t) on the horizontal axis, so the slope of the graph is given by

• Since the rate of change of velocity is termed as acceleration, the slope of a velocity-time graph gives the acceleration.