Average Velocity in 2D Motion

Q. Two point charges $q_1=q_2=+2\mu \text{C}$ are fixed at $x_1=+3\text{m}$ and $x_2=-3\text{m}$ as shown in the figure. A third particle of mass $1\text{g}$ and charge $q_3=-4\mu C$ is released from rest at $y=4\text{m}$. Find the speed of the third particle as it reaches the origin.

1. $5.4\text{m/s}$
2. $6.2\text{m/s}$
3. $7.6\text{m/s}$
4. $8.8\text{m/s}$

Q.

When a person leaves his home for sigthseeing by his car, the meter reads 12352 km, When he returns home after two hours the reading is 12413 km.

(a) What is the average speed of the car during this period?

(b)What is the average velocity.

Q.

A ball of mass $4\mathrm{Kg}$, moving with a velocity of $10{\mathrm{ms}}^{-1}$, collides with a spring of length $8\mathrm{m}$ and force constant $100{\mathrm{Nm}}^{-1}$. The length of the compressed spring is $\mathrm{X}\mathrm{m}$. The value of $\mathrm{X}$, to the nearest integer, is _______

Q. A particle moves with constant speed $v$ along a regular hexagon $ABCDEF$ in the same order. Then the magnitude of the average velocity for it’s motion from $A$ to

1. $F$ is $\frac{v}{5}$
2. $D$ is $\frac{v}{3}$
3. $C$ is $\frac{v\sqrt{3}}{2}$
4. $B$ is $v$

Q. A charged particle $q$ is shot from a large distance towards another charged particle $Q$ which is fixed, with a speed $v$. It approaches $Q$ up to a closest distance $r$ and then returns. If $q$ was given a speed $2v$, the distance of closest approach would be

1. $r$
2. $2r$
3. $\frac{r}{2}$
4. $\frac{r}{4}$

Q.

It is 260 from Patna to Ranchi by air and 320 km by road. An Aeroplane takes 30 minutes to go from Patna to Ranchi Whereas a delux bus takes 8 hours.

(a) Find the average speed of the plane.

(b) Find the average speed of the bus.

(c) Find the average velocity of the plane.

(d) Find the average velocity of the bus.

Q.

A particle is moving in a straight line. Its displacement at time $t$ is given by $s=–4t^2+2t$, then its velocity and acceleration at time $t=1/2$ second are

1. $–2,–5$

2. $2,6$

3. $–2,-8$

4. $2,8$

Q.

The acceleration of a cart started at t =0, varies with time as shown in figure (3-E2). Find the distance travelled in 30 seconds draw the position-tome graph.

Q.

The motion of a particle is defined by the equations $x=4t^2$ and $y=2t^3$ in $meters$, where $t$ is in $seconds$. Determine the normal and tangential components of the particle’s velocity and acceleration when $t=2s$

Q. A particle is projected from the ground with an initial speed of $v$ at an angle $\theta$ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

1. $\frac{v}{2}\sqrt{1+2{\cos }^2\theta }$
2. $\frac{v}{2}\sqrt{1+{\cos }^2\theta }$
3. $\frac{v}{2}\sqrt{1+3{\cos }^2\theta }$
4. $v\cos \theta$

Q.

A train of 150 m in length is going towards the north direction at a speed of 10.5 m/s. A parrot flies at a speed of 4.5 m/s towards the south direction parallel to the railway track. What is the time taken by the parrot to cross the train?

Q. A body is projected with kinetic energy E such that its range is maximum.Its potential energy at the maximum height is

1. 2 K
2. Zero
3. 4 K
4. 3 K

Q. A particle is undergoing circular motion of radius $R$ with angular speed $\omega$. It is brought to rest in $T$ time and then again accelerated to the same angular speed in $\frac{T}{2}$ time. The angular displacement of the particle in this time interval of $\frac{3T}{2}$is (consider uniform acceleration and retardation)

1. $\frac{\omega T}{4}$
2. $\frac{\omega T}{2}$
3. $\omega T$
4. $\frac{3\omega T}{4}$

Q.

The velocity $v$ of a particle at any in moving in a straight line is given by $v=s+1$where $s$ metre is the distance travelled in $t$seconds. What is the time taken by the particle to cover a distance of $9m$?

1. $1s$

2. $\log \left(10\right)s$

3. $2\log \left(10\right)s$

4. $10s$

Q.

A boy walks for 1 minute at a speed of 1 m/s and then runs for 1 minute at a speed of 3 m/s along a straight track. Calculate the average speed of the boy.

Q. If the horizontal range is four times the maximum height attained by a projectile then the angle of projection is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${45}^{\circ }$
4. ${30}^{\circ }$

Q. A spring is stretched by $5\text{cm}$ by a force $10\text{N}$. The time period of the oscillations when a mass of $2\text{kg}$ is suspended by it is

1. $3.14\text{s}$
2. $0.628\text{s}$
3. $0.0628\text{s}$
4. $0.314\text{s}$

Q.

A train moves at a constant speed of 60.0 km/h towards east for 30 min, then in a direction ${30}^{\circ }$ east of due north for 20.0 min, and then west for 45 min. What are the (a) magnitude(in km/min) and (b) angle of its average velocity during this trip?

1. Magnitude=

2. Magnitude=

3. Magnitude=

4. Magnitude=

Q. A swimmer jumps from a bridge over a canal and swims $1\text{km}$ up stream. After that first $\text{km}$, he passes a floating cork. He continues swimming for half an hour and then turns around and swims back to the bridge. The swimmer and the cork reach the bridge at the same time. The swimmer has been swimming at a constant speed. How fast does the water in the canal flow in $\text{km/hr}$?

Q. Statement I: Retardation is directed opposite to the velocity.
Statement II: Retardation is equal to the time rate of decrease of velocity.

1. Both statement 1 and statement 2 are correct and statement 2 is the correct explanation of statement 1.
2. Both statement 1 and statement 2 are correct and statement 2 is not the correct explanation of statement 1.
3. Statement 1 is correct and statement 2 is incorrect.
4. Statement 1 is incorrect and statement 2 is correct.

Q. what is the difference between rectilinear motion and one dimensional motion

Q.

Draw a velocity versus time graph of a stone thrown vertically upwards and then coming downwards after attaining the maximum height.

Q. A car travels with a uniform velocity of $25m{s}^{-1}$ for $5s$ the brakes are then applied and the car is uniformly retarded and comes to rest in further $10s$ find the distance which the car travels before the brakes are applied.

Q.

A stone lying at the edge of a road falls down into a river flowing below the road. If the stone takes $2$ seconds to reach the river, the find (i) the speed with which the stone strikes the water surface in the river, (ii) the average speed of the stone at the end of the fall and (iii) the height of the road from the river. $(Take,g=9.8m{s}^{-2})$

Q. On a foggy day, two drivers spot in front of each other when 80 metre apart. They were traveling at 70 kmph and 60 kmph. Both apply brakes simultaneously which retard the cars at the rate $5\left[m/s^2\right]$ Which of the following statements is correct?

1. The collision will be averted
2. The collision will take place
3. They will across each other
4. They will just collide

Q.

A car travels along a circular track of a radius of 50 m. It takes 20 seconds to complete one rotation.

Calculate (i) speed (ii) Velocity of the car .

Q. Velocity of a particle is given as $V=4-t^2$. If the particle starts its motion from origin then, time after which it will be again at origin is

1. $\sqrt{12}sec$
2. $4sec$
3. $3sec$
4. $\sqrt{15}sec$

Q. Billy jogs $2.5km$ east in $45$ minutes, takes a water break for $12$ minutes, and then walks west at a rate of $0.65km/h$ for $30min$. What is Billy's average velocity? (Answer units: km/hr)

1. $1.52$
   
2. $1.96$
   
3. $2$
   
4. $1.45$
   

Q. Pick the correct option based on following statements.
(A) Average speed of a particle can never be less than the magnitude of average velocity.
(B) We may come across $\left|\frac{d\overrightarrow{v}}{dt}\right|\ne 0$ but $\frac{d}{dt}\left|\overrightarrow{v}\right|=0$.
(C) The average velocity of a particle is zero in a time interval but instantaneous velocity is never zero in that interval.

1. Only A and B are correct
2. Only B and C are correct
3. Only A and C are correct
4. A, B and C are correct

Q.

If a man is driving at an average speed of $xkm/hour$. Find the distance covered in $5hours$.