Uniform Motion

Q. A train travels from a city $A$ to city $B$ with a constant speed of $10\text{m/s}$ and returns back to city $A$ in half of the time taken to travel from $A$ to $B$. Find its average speed during the entire journey.

1. $40\text{m/s}$
2. $30\text{m/s}$
3. $15\text{m/s}$
4. $\frac{40}{3}\text{m/s}$

Q. A body moving with uniform acceleration had velocities of 20 m/s and 30m/s when passing the points P and Q of its path.Find the velocity midway between P and Q(in m/s).

Q. Which of the following statements are incorrect?
(i) Average velocity is path length divided by time interval.
(ii) In general, average speed is greater than the magnitude of the average velocity.
(iii) A particle moving in a given direction with a non-zero velocity can have zero speed.
(iv) The magnitude of average velocity is the average speed.

1. (ii) and (iv)
2. (i), (iii) and (iv)
3. (ii) and (iii)
4. All four

Q. Which of the following four statements is false

1. A body can have zero velocity and still be accelerated
2. A body can have a constant velocity and still have a varying speed
3. The direction of the velocity of a body can change when its acceleration is constant
4. A body can have a constant speed and still have a varying velocity

Q. A vehicle can accelerate or decelerate at a maximum value of $1m{s}^{-2}$ and can attain a maximum speed of $20m{s}^{-1}$. If it starts from rest, what is the shortest time in which it can travel $1000m$, in a straight path, if it has to come to rest at the end of $1000m$?

1. $50s$
2. $70s$
3. $30s$
4. $20s$

Q. A particle has intial velocity of 10m/s due east and a constant acceleration of 2m/s due west . Find the distance travel in first 7sec 1)29 2)21 3)27 4)25

Q. Under what condition is the relation s=ut is correct.

Q. A car is travelling at a speed of $72\text{km/hr}$. Evaluate the value of speed in $\text{m/s}$.

1. $25\text{m/s}$
2. $20\text{m/s}$
3. $10\text{m/s}$
4. $15\text{m/s}$

Q. Which among the following quantities, is always negative for a particle executing S.H.M.? (Symbols have their usual meaning)

1. $\overrightarrow{r}.\overrightarrow{v}$
2. $\overrightarrow{v}.\overrightarrow{a}$
3. $\overrightarrow{a}.\overrightarrow{r}$
4. $\overrightarrow{r}\times \overrightarrow{v}$

Q. A truck has to carry a load in the shortest time from one station to another station situated at a distance $L$ from the first. It can start up or slowdown at the same acceleration or deceleration $a$. What maximum velocity must the truck attain to satisfy this condition?

1. $\sqrt{La}$
2. $\sqrt{5La}$
3. $\sqrt{3La}$
4. $\sqrt{2La}$

Q.

Q. If a body is accelerating:

A. It may speed up

B. It may speed down

C. It may move with same velocity

D. It may move with same speed

Options correct are:

(a) (A, D)

(b) (A, B, D)

(c) (B, C)

(d) (B, C, D)

Q. Two insects Chinki and Minki start to move in from point $A$ in straight line paths in a circle as shown. Chinki travels along $AP$ and Minki along $AM$, on reaching point $M$, Minki insect changes its direction and moves parallel to the line $AP$ and reaches the diametric opposite point $B$. The radius of circle is $5\text{m}$ and line $AP$ makes an angle of ${37}^{\circ }$ with the diameter $AB$. If the speed of Minki insect along $AMB$ is $2\text{m/s}$ constant then how much time (in $\text{sec}$) will Minki take to reach $B$ from $A$.

Q. A car is travelling at a speed of $20\text{m/s}$. Evaluate the value of speed in $\text{km/hr}$.

1. $48\text{km/hr}$
2. $36\text{km/hr}$
3. $72\text{km/hr}$
4. $54\text{km/hr}$

Q. Inspector Ram Singh on a police jeep is chasing a culprit, going on a motorcycle. The motorcycle crosses a turning at a speed of $72km/h$. The jeep follows it at a speed of $90km/h$, crossing the turning 10 seconds later than the motorcycle. Assuming they travel at constant speeds, how far(in km) from the turning will Ram Singh catch up with the culprit?

Q. A particle moving with a uniform acceleration travels 24m and 64m in first two successive intervals of 4sec each. Whats its initial velocity?

Q. For uniform motion, both magnitude and of velocity must remain constant.

1. strength
2. direction
3. speed

Q. Which of the following equations does not represent a simple harmonic motion

1. $y=\alpha \omega t$
2. $y=\alpha \omega t+bcos\omega t$
3. $y=\alpha tan\omega t$
4. $y-\alpha \omega t$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

A girl goes on morning walk with her father. She starts from a point P and reaches to point Q in one-fourth of an hour and returns to her starting point in 30 minutes. If the separation between point P and Q is 3 km, then choose the correct statement(s) regarding her entire journey.

एक लड़की अपने पिता के साथ प्रातःकाल के भ्रमण पर जाती है। वह एक बिंदु P से गति करना प्रारम्भ करती है तथा 15 मिनट में बिंदु Q पर पहुँचती है तथा अपने प्रारम्भिक बिंदु पर 30 मिनट में वापस लौटती है। यदि बिंदु P तथा Q के मध्य दूरी 3 km है, तब उसकी सम्पूर्ण यात्रा के सन्दर्भ में सही कथन/कथनों का चयन कीजिए।

1. Her motion is uniform
   
   उसकी गति एकसमान है
   
2. Her motion is non-uniform
   
   उसकी गति अ-समान है
   
3. Her average speed is 8 km/h
   
   उसकी औसत चाल 8 km/h है
   
4. Her average speed is $\frac{20}{9}m/s$
   
   उसकी औसत चाल $\frac{20}{9}m/s$ है
   

Q. State whether given statement is True or False.
A body can have constant velocity and still have varying speed?

1. True
2. False

Q. A particle is moving in a straight line whose velocity at x= 2 m is 3 m/s. If position of the particle varies with acceleration as a= 2x, where a and x are in SI units, then the velocity of particle at x = 5 m is

Q. An aeroplane flies 400 m North and 300 m South and then flies 1200 m upwards then net displacement is

1. 1500 m
2. 1204.15 m
3. 1300 m
4. 1400 m

Q. A particle covers half of its total distance with speed, $v_1$ and the rest half distance with speed, $v_2$. Its average speed during the complete journey is

1. $\frac{v_1+v_2}{2}$
2. $\frac{v_1{v}_2}{v_1+v_2}$
3. $\frac{2v_1{v}_2}{v_1+v_2}$
4. $\frac{2v_1^2{v}_2^2}{v_1^2+v_2^2}$

Q. A $150\text{m}$ long train is moving with a uniform velocity of $45\text{km/h}$. The time taken by the train to cross a bridge of length $850\text{m}$ is

1. 56 sec
2. 68 sec
3. 80 sec
4. 92 sec

Q. For uniform motion, both magnitude and of velocity must remain constant.

1. strength
2. direction
3. speed

Q. At time t = 5 secs, the elevator will be on thefloor if nobody stops the elevator and there are enough floors in the building.

1. 8th
2. 10th
3. 11th
4. 12th

Q. A body covers a total distance of $S$. Initial $\frac{S}{3}$ is covered with speed 10 km/hr and next $\frac{2S}{3}$ is with $v$. If average speed is 8 km/hr, find $v$.

1. 6 km/hr
2. 5.2 km/hr
3. 7.2 km/hr
4. 4.2 km/hr

Q. A particle starting with certain initial velocity and uniform acceleration covers a distance of $12m$ in first $3s$ and a distance of $30m$ in next $3s$. The initial velocity of the particle is

1. $3m{s}^{-1}$
2. $2.5m{s}^{-1}$
3. $1.5m{s}^{-1}$
4. $2m{s}^{-1}$
5. $1m{s}^{-1}$

Q. A passenger train takes $2$ hours more than an express train to travel a distance of $240km$. The speed of the express train is more than that of passenger train by $20km/h$. Find the speed of both the trains.

Q.

A car moving with a speed of $40km/hr$ can be stopped by applying breaks for $2$ km. If the same car is moving with a speed of $80km/hr$, what is the minimum stopping distance? Assume constant retardation.

1. $8Km$
2. $2Km$
3. $4Km$
4. $6Km$

Q.

The displacement of a particle is given by $\overrightarrow{r}=A(\overrightarrow{i}cos\omega t+\overrightarrow{j}sin\omega t)$The motion of the particle is

1. simple harmonic

2. on a straight line

3. on a circle

4. with constant acceleration