Multiple Choice

Pick the correct statements:

AAverage speed of particle in a given time is never less than the magnitude of the average velocity.
Correct Answer
BIt is possible to have a situation in which $$\left| \cfrac { d\vec { v } }{ dt } \right| \neq 0 $$ but $$\cfrac { d }{ dt } \left| \vec { v } \right| =0$$.
Correct Answer
CThe average velocity of a particle is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval
Correct Answer
DThe average velocity of a particle moving on a straight line is zero in a time interval. It is possible that the instantaneous velocity is never zero in the interval. (Infinite accelerations are not allowed).

Solution

Distance is greater than or equal to displacement.
Hence, average speed is greater than or equal to the average velocity.
(A) is correct

In uniform circular motion,
$$\left| \dfrac{d\vec v}{dt} \right| = \omega^2 R \neq 0$$
$$\dfrac{d|\vec v|}{dt} = 0$$ as $$|\vec v|$$ is constant
(B) is correct

In uniform circular motion, instantaneous velocity is never zero but average velocity in the time period of rotation is zero.
(C) is correct

If average velocity of a particle is zero, its net displacement is zero. This can happen in a straight line motion only in two ways-
1. The particle is at rest.
2. The particle reverses its direction at-least once in the time interval.
Both the scenarios demand that the instantaneous velocity is zero atleast once in the time-interval.
(D) is wrong.

SIMILAR QUESTIONS

Kinematics

An objective having a velocity $$4.0\ m/s$$ is acceleration at the rate of $$1.2\ m/s^2$$ for $$5.0\ s$$. Find the distance travelled during the period of acceleration.

Kinematics

A particle moves along $$x$$-axis as follows: It starts from rest at $$t=0$$ from a point $$x=0$$ and comes to rest at $$t=1$$ at a point $$x=1$$. No other information is available about its motion for the intermediate time $$0

Kinematics

A body starts from rest, with uniform acceleration a. The acceleration of a body as function of time t is given by the equation $$a=pt$$ where p is constant, then the displacement of the particle in the time interval $$t=0$$ to $$t=t_1$$ will be?

Kinematics

For a particle moving in a straight line, the velocity at any instant is given by $$4t^3-2t$$, where t is in second and velocity in m/s. The acceleration of the particle when it is $$2$$m from the starting point, will be?

Kinematics

A particle moves as such whose acceleration is given by $$a=3\sin 4t$$, then:

Kinematics

A particle P is at the origin starts with velocity $$\vec{u}=(2\hat{i}-4\hat{j})$$m/s with constant acceleration $$(3\hat{i}+5\hat{j})m/s^2$$. After travelling for $$2$$ second, its distance from the origin is?

Kinematics

A body initially at rest is moving with uniform acceleration a. Its velocity after n seconds is v. The displacement of the body in last 2 s is :

Kinematics

An auto travelling along a straight road increases its speed from 30.0 m $$s^{-1}$$ to 50.0 m $$s^{-1}$$ in a distance of 180 m. If the acceleration is constant, how much time elapses while the auto moves this distance?

Kinematics

A particle $$A$$ moves in one direction along a given trajectory with a tangential acceleration $$\omega_\tau=a\tau$$, where $$\vec{a}$$ is a constant vector coinciding in direction with the $$x$$ axis as shown in figure above, and $$\vec{\tau}$$ is a unit vector coinciding in direction with the velocity vector at a given point. Find how the velocity of the particle depends on $$x$$ provided that its velocity is negligible at the point $$x=0$$.

Kinematics

the same dependence of the velocity and the acceleration of the particle;

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