# Instantaneous Velocity

## Trending Questions

**Q.**

The position vector of a particle →R as a function of time is given by →R=4sin(2πt)^i+4cos(2πt)^j, where R is in meters, t is in seconds and ^i and ^j denote unit vectors along 'x' and 'y'-directions respectively. Which one of the following statements is wrong for the motion of particle?

- Path of the particle is a circle of radius 4 m
- Acceleration vector is along −→R
- Magnitude of acceleration vector is v2R, where v is the velocity of particle
- Magnitude of the velocity of particle is 8 ms−1

**Q.**

A particle moves along a straight line $OX$. At a time $ts$, the distance $xm$ of the particle from $O$ is given by $x=40+12t\xe2\u20ac\u201c{t}^{3}$. How long would the particle travel before coming to rest?

$24m$

$40m$

$56m$

$16m$

**Q.**A particle is moving with speed v=b√x along the positive x - axis. Calculate the speed of the particle at time t=τ. (Assume that the particle is at the origin at t=0).

- b2τ2
- b2τ
- b2τ√2
- b2τ4

**Q.**

A particle is moving along a circular path of radius 5m with a uniform speed 5m per second. What will be the average acceleration when the particle completes half revolution?

**Q.**The kinetic energy of a projectile at the highest point is half of the initial kinetic energy. What is the angle of projection with the horizontal?

- 45∘
- 30∘
- 60∘
- 90∘

**Q.**

Explain the terms the average velocity and instantaneous velocity. When are they equal?

**Q.**A particle of mass 2 gm and charge 1 μC is held at rest on a frictionless horizontal surface at a distance of 1 m from the fixed charge of 1 mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of 10 m from the fixed charge is

- 45 ms−1
- 60 ms−1
- 90 ms−1
- 100 ms−1

**Q.**The intensity ratio of two waves is 9 : 1. These wave produce interference. The ratio of maximum intensity to minimum intensity will be

- 1 : 9
- 9 : 1
- 1 : 4
- 4 : 1

**Q.**The two ends of train moving with constant acceleration pass a certain point with velocities u and 3u the velocity with which middle point of the train passes the same point

**Q.**A point charge +Q having mass m is fixed on horizontal smooth surface. Another point charge having magnitude +2Q and mass 2m is projected horizontal towards the charge +Q from far distance with velocity vo.

Acceleration of the particle +2Q when it is closest to fixed particle +Q :

- Zero
- mv4o2kQ2
- mv4o4kQ2
- mv4okQ2

**Q.**

A person traveling at 43.2 km/h applies the brake giving a deceleration of 6.0 m/s2 to his scooter. How far will it travel before stopping?

**Q.**

The numerical ratio of average velocity to average speed is.

always less than one

always equal to one

always more than one

equal to or less than one

**Q.**A beam of unpolarized light of intensity I0 is passed through a polaroid A and then through another polaroid B. Polaroid B is oriented so that its principal plane makes an angle of 45∘ relative to that of A. The intensity of the emergent light is,

- I0
- I0/2
- I0/4
- I0/8

**Q.**A point charge q having mass m is projected from a long distance with speed v towards another stationary particle of same mass and charge. The distance of closest approach of the particles is :

q22πε0mv2

2q2πε0mv2

- q2πε0mv2
- Zero

**Q.**

An aeroplane flying 490 m above ground level at 100 m/s, releases a block. What horizontal distance would it travel before it hits the ground?

0.1

*km*0.5 km

1

*km*2

*km*

**Q.**Rest mass energy of an electron is 0.51 MeV. If this electron is moving with a velocity 0.8 c (where c is velocity of light in vacuum), then kinetic energy of the electron should be.

- 0.28 MeV
- 0.34 MeV
- 0.39 MeV
- 0.46 MeV

**Q.**Column - I gives a list of possible set of parameter measures in some experiments. The variations of the parameters in the form of graphs are shown in Column - II. Match the set of parameters given in Column - I with the graphs given in Column - II.

- A→p, s;B→q, s;C→s;D→q
- A→p, r;B→q, r;C→s;D→q
- A→p, r;B→q, s;C→r;D→q
- A→p, s;B→q, s;C→s;D→p

**Q.**A beam of natural light falls on a system of 5 Polaroids, which are arranged in succession such that the pass axis of each Polaroid is turned through 60∘ with respect to the preceding one. The fraction of the incident light intensity that passes through the system

- 164
- 132
- 1512
- 1128

**Q.**

A particle moves on xy plane. Its position vector at any time t is →r={(2t)^i+(2t2)^j}m. The rate of change of θ at time t=2 second. (Where θ is the angle which its velocity vector makes with positive x-axis) is

**Q.**

When the distance travelled by an object is directly proportional to the time, it is said to travel with

zero velocity

Constant speed

constant acceleration

uniform velocity

**Q.**A car is moving along a straight line OP . it moves O to P I n 18sec and returns from P to Q in 6sec . where OP =360m and OQ=240m. What are the average velocity and average speed of the car in going: (1) From O to P (2) O to P and back to Q.

**Q.**

A particle moves so that $S=6+48t-{t}^{3}$. The direction of motion reverses after moving a distance of

$63$

$104$

$134$

$288$

**Q.**A clock has its second hand 2.0 cm long.Find the average speed and modulus of average velocity of the second hand in 15s.

**Q.**What is the velocity of projectile when it mooves perpendicular to initial velocity?

**Q.**

If youre driving one and a half miles per minute, slow down by $15$ miles per hour, and then reduce your speed by one third, how fast are you going now?

**Q.**The rotation of the earth having radius R about its axis speeds up to a value such that a man at latitude of 60∘ feels weightlessness. The duration of the day in such a case is

- π√Rg
- π2√Rg
- π3√Rg
- 2√gR

**Q.**

A body starts from a point O with velocity *v *and acceleration *a. *The direction of acceleration is reversed when the velocity becomes *5v. *The velocity of the body at point O will be

-v

-5v

-7v

-9v

**Q.**A particle moves according to the equation x=2t2−5t+6 where, x is in m. Find

(i) average velocity in the first 3 s, and

(ii) instantaneous velocity at t=3 s.

- 2 m/s, 5 m/s
- 1 m/s, 7 m/s
- 4 m/s, 3 m/s
- 3 m/s, 7 m/s

**Q.**

Figure shows the graph of the x-coordinate of a particle going along the X-axis as a function of time. Find

(a) The average velocity during 0 to 10 s,

(b) Instantaneous velocity at 2, 5, 8 and 12s

**Q.**A satellite is revolving around the earth in a circular orbit of radius 'a' with velocity v0. A particle is projected from the statellite in forward direction wiht relative velocity V=[(√54)]v0. During the subsequent motion of the particle, match the following:

Column IColumn III. Total energy of particleP.(−3GMem)8aII. Minimum distance ofQ.(−5GMem)8a particle from the earthIII. Maximum distance ofR.5a3 particle from the earthS. 2aT.2a3U. a

- I→P;II→U;III→S
- I→Q;II→S;III→R
- I→P;II→U;III→R
- I→Q;II→S;III→U