Non Uniform Motion & Avg Velocity

Q. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

1. 4.0 m/s
2. 5.0 m/s
3. 5.5 m/s
4. 4.8 m/s

Q. A body covers 12 m in 2nd second and 20 m in 4th second . Find what distance the body will cover in 4 seconds after the 5th second.

Q.

The distance between Delhi and Agra is 200km a train travels the first 100km at speed of 50km/h how fast must the train travel next 100km so that the average speed is 70km/h for the whole journey

Q.

Between the two stations, a train accelerates from rest uniformly at first, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken be $1:8:1$ and the maximum speed attained be $60\text{km/h}$, then, what is the average speed over the whole journey?

1. $48\text{km/hr}$
2. $52\text{km/hr}$
3. $54\text{km/hr}$
4. $56\text{km/hr}$

Q. A particle is moving on a circular path with constant speed V. It moves between two points A and B, which subtends an angle 60 degree at the centre of circle. Find the magnitude of change in its velocity and change in magnitude of its velocity during motion from A to B.

Q.

A man walks on a straight road from his home to a market 2.5 km away with a speed of $5km{h}^{-1}$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5km{h}^{-1}$. What is the
a) magnitude of average velocity, and
b) average speed of the man over the interval of time (i) 0 to 30 min, (ii) 0 to 50 min,
(iii) 0 to 40 min? [Note: You will appreciate from this exercise why it is better to define average speed as total path length divided by time, and not as magnitude of average velocity. You would not like to tell the tired man on his return home that his average speed was zero!]

Q. A truck driver drives $20km$ down the road in 5 minutes. He then reverses and drives $12km$ back down the road in 3 minutes. What is his average velocity?

1. $4km/min$
2. $2km/min$
3. $3km/min$
4. $60km/h$

Q.

Why circular motion is called accelerated motion ?

Q.

A particle is constrained to move on a straight line path it returns to the starting point after $10sec$. The total distance covered by the particle during this time is $30m$. Which of the following statements about the motion of the particle is false

1. Displacement of the particle is zero

2. Average speed of the particle is $3m/s$

3. Displacement of the particle is $30m$

4. Both $\left(A\right)$ and $\left(B\right)$

Q.

A projectile is fired at ${30}^{\circ }$ to the horizontal. The vertical component of its velocity is $80m{s}^{-1}$. Its time of flight is T. What will be the velocity of the projectile at $t=\frac{T}{2}$

1. 

2. 

3. 

4. 

Q. The position of the particle moving on $X$-axis is given by, $X=A{t}^3+B{t}^2+Ct+D.$ The numerical values of $A,B,C,D$ are $1,4,-2$ and $5$ respectively and SI units are used. Find the average velocity during the interval $t=0$ to $t=4s$.

1. $40\frac{m}{s}$
2. $30\frac{m}{s}$
3. $25\frac{m}{s}$
4. $35\frac{m}{s}$

Q.

A person travels along a straight road for half the distance with velocity $v_1$ and the remaining half distance with velocity $v_2$ The average velocity is given by

1. 

2. 

3. 

4. 

Q. Graph of $\frac{1}{v}vs.x$ for a particle under motion is as shown, where $v$ is velocity and $x$ is position. The time taken by particle to move from $x=4mtox=12m$ is,

1. 12 $sec$
2. 10 $sec$
3. 8 $sec$
4. $\frac{16}{3}$ $sec$

Q.

A particle moves with a uniform velocity

1. The particle must be at rest.

2. The particle moves along a curved path.

3. The particle moves along a circle.

4. The particle moves along a straight line.

Q. the velocity- time relation of a body starting from rest is given by v=k2t3/2 , where k= 2 . the distance traversed in 4 seconds is

Q. The acceleration time graph of a body is shown below.

Which of the following represents the velocity time graph of the motion?

1. 
2. 
3. 
4. None of the above

Q. A particle moving in a straight line covers half the distance with speed of $3m/s$. The other half of the distance is covered in two equal time interval with speed of $4.5m/s$ and $7.5m/s$ respectively. The average speed of the particle during this motion is

1. $4.0m/s$
2. $5.0m/s$
3. $5.5m/s$
4. $4.8m/s$

Q. A boy swims in a 100 m long pool he covers 60 m with a velocity of 20 m/s and covers the rest of the distance with a velocity of 10 m\s. Calculate the average velocity of the boy?

Q. For a body undergoing uniform circular motion, we say it's velocity changes continuously, then does it increase or decrease?

Q.

A, B, C, D are the points in a vertical line, the lengths AB=BC=CD . If the body Falls from rest at A , prove that the times of describing AB, BC, CD are as 1:√2-√1:√3-√2 .

Q. From the adjoining graph, the distance traversed by particle in $4\text{seconds}$, (in $\text{m}$) is

Q.

Assertion- Magnitude of average velocity is equal to average speed, if velocity is constant.

Reason- If velocity is constant, then there is no change in direction of motion.

Q.

Two towns A and B are connected to a regular bus service with a bus leaving in either direction every T min. A man cycling with a speed of 20 km/hr in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and in every 6 min in the opposite direction. What is the period T of the bus service and with what speed do the bus ply on the road?

Q. A particle is moving in a circle of radius r having centre o with a constant speed v.the magnitude of change in velocity moving from a to b is

Q.

The speed of cyclist is 10m/s and speed of wind is 4m/s.can the speed of wind relative to the speed of cyclist be 10m/m?

Q.

Two escalators move people up and down between floors of a shopping mall at the same rate, either up or down. What are the following statements regarding the motion of the escalators being true?

Q. If a car covers $\frac{2}{5^{th}}$ of the total distance with $v_1$ speed and $\frac{3}{5^{th}}$ distance with $v_2$ then average speed is

1. 
2. 
3. 
4. 

Q.

A body covers half the distance with a speed of 20 m/s and the other half with a speed of 30 m/s. The average velocity of the body during the whole journey is

1. zero

2. 24 m/s

3. 25 m/s

4. None of these

Q. A particle is moving in $x-y$ plane along a path $y=x^2+x.$ The ratio $v_y/v_x$, when the particle is at $(2,6)$ is,

$\text{where}\left\{{}_{v_x\to x-\text{component of velocity}}^{v_y\to y-\text{component of velocity}}\right\}$

1. $13$
2. $5$
3. $10$
4. $4$

Q. If position x=t3 2t + 5(m) then velocity at time t = 2 s is?