Relative Position

Q.

The displacement of a particle starting from rest (at t = 0) is given by s = 6t²-t³
The time in seconds at which the particle will attain zero velocity again, is

1. 6

2. 2

3. 8

4. 4

Q. A body executing SHM when its displacement from the mean position is 4cm and 5cm , the corresponding velocity of the body is 10cm/sec and 8cm/sec .Then the time period of the body is (in terms of pi)

Q. a particle is moving along a straight line and its position is given by the relation x=(t^3-6t^2-15t+40)mfind the time at which velocity is zero also position and displacementof the particle at that poi

Q. A ball is projected vertically upward from the ground it takes 4s to reach a point p still moving upward if it takes 10s further to reach to ground then height of point p is

Q. A car is moving with speed 20m/s.Suddenly the driver sees the sign of danger at a distance of 50m.What is the maximum allowable reaction time for him if brakes can produce retardation of 5m?

Q. The displacement x of a body in motion is given by x = a sin(ωt+θ). The time at which the displacement is maximum is:

Q.

A particle executing SHM completes 1200 oscillations per minute and passes the mean position with a velocity of 3.14 m/s.to find the maximum displacement of a particle from the mean position .also obtain the displacement equation of the particle if its displacement is zero at instant t=0.

Q. ntA boat is heading at angle 127^° from the direction of flow. The velocity of boat in water is 5km/hr. The velocity of flow of water is 4km/hr. The displacement of boat along the flow of water, is (width of the river is 1200m)n nt1) 250mn nt2) 300mn nt3) 350mn nt4) 400mn

Q. a bird flies to and fro between two cars which are moving towards each other with cons†an t speed 10km/h each. if initial seperation between cars is 100km and bird has a cons†an t speed 25km/h. the displacement of bird when both cars meet is

Q. 9. How to prove equation of trajectory of projectile motion

Q. 14.) A ball falls on an inclined plane of inclination theta from aheight h above the point of impact and makes a perfectly elastic collision. Where will it hit the plane again?

Q. 3.A block of 3kg rests in limiting equilibrium on an inclined plane of inclination 30degrees. If the inclination of the plane is increased to 60degree , the minimum force along the plane required to keep it stationary

Q. 19. If the displacement of an object during its motion is 100m in a time interval of 20s then calculate the avg velocity of objects with which it was moving through out his journey

Q. A man is $25\text{m}$ behind a bus, when the bus starts accelerating at $2{\text{m/s}}^2$ and man starts moving with constant velocity of $10\text{m/s}$. Time taken by him to board the bus is

1. $2\text{s}$
2. $3\text{s}$
3. $4\text{s}$
4. $5\text{s}$

Q. a person rows a boat in water with a speed if 4m/s. Water in the river is flowing with a speed of 2m/s . If the person rows prependicular to the direction of flow, find the resul†an t velocity of boat and time taken by the boat to cross the river if width of the river is 400m

Q. 34. A man running at speed 5km/ hr finds the rain hitting his head vertically but he has to hold umbrella at 30 degree while at rest. The speed of rain is

Q. 119. How to prove equation of trajectory of projectile motion

Q. The relation between position (x) and time (t) are given below for a particle moving along a straight line. Which of the following equation represents uniformly accelerated motion? \lbrack where α and β are positive cons†an ts\rbrack 1. β x = α t + αβ 2. α x = β + t 3. xt = αβ 4. α t = \sqrt{β +

Q. A person driving a car with a speed 72km/h, suddenly sees a boy crossing the road . If the distance moved by car, before the person applies brakes is 5m, the reaction time if the person i

Q. Two particles A and B travells along the X-y axis with respective constant velocity V1= i m/s and V2= 2j m/s at time t=0. there at position (-2.0)m and (0, 1)m respectively. the position vector of particle B with respect to A at 3 sec will be

Q. A man is $d$ distance behind a bus. The bus starts moving away from the man with an acceleration $a$. At the same time man starts running towards the bus with a constant velocity $v$.

1. The man catches the bus if $v\ge \sqrt{2ad}$
2. If man just catches the bus, the time of catching the bus will be $t=\frac{v}{a}$
3. If man just catches the bus, the time of catching the bus will be $t=\frac{2v}{a}$
4. The man will catch the bus if $v\le \sqrt{ad}$

Q. what happens if absolute rest is possible?

Q. A particle is moving along a straight line. Its velocity varies as v = 6 – 2t where v is in m/s and t in seconds. Find the difference between distance covered and magnitude of displacement in first 4 seconds.

Q. 69.If a particleof mass M starting from rest undergo uniform acceleration. If the speed acquired in time T is V then power delivered to the particle is

Q.

Two bodies move towards each other from 10 m apart with a constant velocity they meet at C after 2s. What is the displacement of B w.r.t. A?

1. -6 m

2. -10 m

3. 6 m

4. 10 m

Q. 30.Two particle of equal mass have coordinate (2m, 4m, 6m) and (6m, 2m, 8m ). Of these one particle has a velocity of v1= 2i and other has velocity v2= 2j at t=0 . The coordinate of centre of mass at time t=1 will be 1) (4m , 4m , 7m ) 2) (5m , 4m , 7m ) 3) (2m , 4m , 6m ) 4) (4m , 5m , 4m )

Q. Paragraph for below question
नीचे दिए गए प्रश्न के लिए अनुच्छेद

When an object follows a circular path at constant speed, the motion is called uniform circular motion. When taking centre of circle at origin, the equation of circle is x² + y² = r², where r is radius of circle. The velocity of the object is continuously changing in direction and object undergoes acceleration.

In uniform circular motion, magnitude of acceleration towards centre of circle is $\left(\frac{v^2}{r}\right)$. Now answer the following question.

जब एक वस्तु नियत चाल से वृत्तीय पथ का अनुसरण करती है, तब गति को एकसमान वृत्तीय गति कहा जाता है। जब वृत्त के केन्द्र को मूल बिन्दु पर लिया जाता है, तब वृत्त की समीकरण x² + y² = r² है, जहाँ r वृत्त की त्रिज्या है। वस्तु के वेग की दिशा मे निरन्तर परिवर्तन हो रहा है तथा वस्तु त्वरित होती है।

एकसमान वृत्तीय गति में, वृत्त के केन्द्र की ओर त्वरण का परिमाण $\left(\frac{v^2}{r}\right)$ है। अब निम्नलिखित प्रश्न का उत्तर दीजिए।

Q. The acceleration (in m/s²) of the particle, when it is at point (5 m, 5 m) is

प्रश्न - जब कण बिंदु (5 m, 5 m) पर है, तब इसका त्वरण (m/s² में) है

1. $\hat{i}-\hat{j}$
2. $-\hat{i}-\hat{j}$
3. $\frac{1}{\sqrt{2}}\hat{i}-\frac{1}{\sqrt{2}}\hat{j}$
4. $-\frac{1}{\sqrt{2}}\hat{i}-\frac{1}{\sqrt{2}}\hat{j}$

Q. A person driving a car with a speed72km/hr, suddenly sees a boy crossing the road.if the distance moved by car, before the person applies brake is 5m the reaction time of the person is

Q. The velocity-time graph for the motion of two cars A and B, moving in the same direction along a straight path is shown in figure. If both cars start from rest at the same point and have acceleration 2 m/s² up to a speed of 20 m/s. Now both of them continue at constant speed of 20 m/s. If A has travelled 36 m at the instant when B starts, then the distance between A and B, when the speed of B reaches 20 m/s is

चित्र में सरल पथ के अनुदिश समान दिशा में गतिमान दो कारों A व B की गति के लिए वेग-समय आरेख दर्शाया गया है। यदि दोनों कारें समान बिंदु पर विराम से गति प्रारम्भ करती हैं तथा इनमें 20 m/s की चाल तक 2 m/s² का त्वरण होता है। अब ये दोनों 20 m/s की नियत चाल से निरन्तर गति करती हैं। यदि B के प्रारम्भ होने के क्षण पर A द्वारा 36 m की दूरी तय कर ली जाती है, तब B की चाल 20 m/s होने पर A व B के मध्य दूरी है

1. 220 m
2. 100 m
3. 120 m
4. 320 m

Q. A particle starting from point A on a circular path, travelling upto point B with constant speed v₁, then upto point C with constant speed v₂ and finally upto point A with constant speed v₃ as shown below. If particle covers each part of the path in equal intervals of time, then

एक कण वृत्तीय पथ पर बिंदु A से गति करना प्रारम्भ करता है, यह नीचे दर्शाए अनुसार नियत चाल v₁ से बिंदु B तक, फिर नियत चाल v₂ से बिंदु C तक तथा अन्त में नियत चाल v₃ से बिंदु A तक गति करता है। यदि कण पथ का प्रत्येक भाग समान समयान्तराल में तय करता है, तब

1. v₃ > v₁
2. v₂ > v₃
3. v₁ > v₂
4. v₁ > v₃