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Syllabus

Derive equations of motion?

^{2}, car B starts from rest with acceleration of 2 m/s^{2 1)as seen by passenger in car A a) first , car B moves backward and then forward b)}first , car B moves forward and then backwardState and prove triangle law of vector addition.

A police constable is chasing a thief who is initially 10m ahead of the constable.The uniform speeds of the constable and the thief are 10m/s and 8 m/s respectively.From the plot of the position time graph for the constable and the thief ,find the time the constable will take to catch the thief and the distance the constable has to run.

What is galileo law of odd numbers????

the position of a body moving along x-axis at time t is given by

x = (tm . The distance travelled by body in time interval t = 0 to t = 3 s is -^{2}-4t+6)(1) 5 m

(2) 7m

(3) 4 m

(4) 3 m

A ball is thrown vertically upwards with a velocity of 20m/s from the top of a multistorey building. The height of the point from where the ball is thrown is 25m from the ground.

(1) How high the ball will rise?

(2) How long it will be before the ball hits the ground? (Take g=10m/s

^{2}a block of mass of 2 kg is placed on the floor. the coefficient of static friction is 0.4 . a force F of 2.5 N is applied on the block. calculate the force of friction between the block and the floor.

a bicyclist encounters a series of hills.uphill speed is always v1 and downhill speed is always v2.the total distance travelled is l,with uphill and downhill portions of equal length,the cyclist's average speed is

1.v

_{1}/v_{2}2.v

_{2}/v_{1}3.v

_{1}v_{2}/v_{1}+v_{2}4.2v

_{1}v_{2}/v_{1}+v_{2}means & full form of w.r.t.

two trains one travelling at 72 km/h and other at 90 km/h are heading towards one another along a straight level track. when they are 1.0km apart both the drivers simultaneously see the other's train and apply brakes which retard each train at the rate of 1.0m/s. determine whether the trains would collide or not.

a ball is thrown vertically upward with a speed of 19.6 m/s from the top of a tower and returns to earth in 6 sec find the height of the tower

a) 0.5m b)9.5m c)81m d)90m

A particle is moving east-wards with a velocity of 5m/s. in 10 seconds the velocity changes to 5 m/s northwards.What is the average acceleration in this time ?

The acceleration-time graph of a body starting from rest is shown below. Calculate the

(1) Average acceleration

(2) Average velocity

(3) Average speed in the time interval t = 0 to t = 40 s

find unit vector perpendicular to

A=2 i +j + k andB= i-j+2k.A car is being driven at a uniform velocity 'u' on a horizontal road. The driver suddenly puts his foot on the accelerator and the speed increases to 'v'. Unfortunately after that his break failed. Show his velocity-time graph.

if a particle starts moving with acceleration 2m/s2 . what is th distance travelled by it in 5th half second ?

find the vector having a magnitude 3 units in the direction of the resultant vector of the vector addition of vector A and vector B.vector A=i cap+ j cap; vector B=k cap

A stone falls freely from rest & the total distance covered by it in last second of its motion equals the distance covered by it in the first 3second of its motion.How long the stone will remain in the air?please show me easy processes.

speed of train is increasing linearly with time .the train passes the hut with the speed 2m per sec and acquires a speed of 12 m per sec after 10 sec . what is the speed of the train in m/s ,5 sec after passing the hut.

a train starts from a station with acceleration 0.2 m/s

^{2}on a straight track and then comes to rest after attaining maximum speed on another station due to retardation 0.4m/s^{2}. if total time spent is half an hour, then distance between two stations is {neglect length of train}1. 216 km

2. 512 km

3. 728 km

4. 1296 km

If the acceleration of a particle is constant in magnitude but not in direction what type of path does the particle follow?

A balloon starts rising from the ground with acceleration of 1.25m/s sq . After 8s a stone is released from the balloon . How much time will it take to reach the ground ?(g = 10 m/s sq. )

the resultant of 2 vectors u and v is perpendicular to u and its magnitude is equal to half of v find the angle between u and v?

A ballon is ascending at the rate of 14m/s at a height of 98m above the ground when a packet is dropped from the ballon.After how much tym and with wat velocity does it reach the ground?

Assume that the throwing speed (u) is same in both cases.

two parallel rail tracks run north -south. train A moves north with speed 54km/h and train B moves south with speed 90km/h. what is the velocity of a monkey running on roof of a train A against its motion (with velocity of 18km/h with respect to A)as observed by a man standing on ground(in m/s).

A) speed of A = Speed of B = speed of C B) speed of b > speed of a > speed of c

c)speed of b < speed of a < speed of c d)speed of a < speed of b = speed of c

Water drops fall at regular intervals from tap 5m above the ground.The third drop is leaving the tap at the instant the first drop touches the ground.How far above the ground is the second drop at that instant?

A ) 1.25m

B ) 2.5m

C ) 4.25m

D ) 2.25m

E ) 3.75m

(A) $\frac{200}{3}$ km/hr

(B) $\frac{100}{3}$ km/hr

(C) 200 km/hr

(D) 150 km/hr

A car accelerates from rest at a constant rate α (alpha) for some time. After which it decelerate at a constant rate β (beta) to come to rest . If total time elapsed is t second then calculate total distance travelled by the car in term of α.βOn a two lane road, car A is travelling with a speed of 36km/h . two cars B and C approach car A in opposite directions with a speed of 54km/h each. At certain instant ,when the distance AB is equal to AC , both being 1 km , B decides to overtake A before C does. what minimum acceleration of car B is required to avoid an accident ?

Q9. A particle is moving along a straight line such that its velocity varies with position as shown in figure, then the acceleration of the particle at x = 10 m is

(1) – 4.6 m/s

^{2}^{ }(2) –6.8 m/s^{2}(3) –8.9 m/s

^{2}(4) – 10.6 m/s^{2}A particle is moving along a circle such that it completes one revolution in 40 sec.

in 2 min 20 sec, the ratio |displacement| /distance is...???Under what condition , does the relationship delta x = v.delta t holds good .Plz explain.

two trains A and B of length 400m each are moving on two parallel tracks with a uniform speed of 72 km/h in the same direction,with A ahead of B.The driver of B decides to overtake A andaccelerates by 1m/s^2.If after 50s ,the guard of B just brushes past the driver of A,what was the original distance between them?

^{2}-3t^{3}. Determine:(a) the average velocity during the interval t=0 to t=4 seconds

(b) the instantaneous velocity at t=1 second

(c) the instants and positions of the body at which it is at rest

(d) the acceleration at t=4 seconds

(e) the average acceleration during the time interval t=1 to t=3 seconds

If unit vectors A and B are inclined at an angle theta, then prove that IA-BI=2 sin theta/ 2

A body is dropped from the top of a tower through 40 m during the last two seconds of its fall.Waht is the height of the tower.

g=10 ms^{-1}Q. The position of an object moving along x-axis is given by x= a + btwhere a=8.5m, b=2.5m/s

^{2}^{2}and t is measured in seconds. What is its velocity at t=0s and t=2.0s. What is the average velocity b/w t=2.0s and t= 4.0s ?pls reply soon1. v = u + αt3/2

2. v = u + 3/2αt3

3. v = u +2/5αt5/2

4. v = u + αt5/2

_{0}=+ve,v=+veb)x_{0}=+ve,v=-vec)x_{0}=-ve,v=+ved)x_{0}=-ve,v=-veThe letters x_{0}and v represent postion of the object at t=0 and uniform velocity of the object respectively.3.Two ends of a train moving with a constant acceleration passes a certain point with elocities u and v. Show that the elocity with which the middle point f the train passes the same point is square root of(u^{2}+v^{2})/2.The acceleration-time graph of a particle moving along a straight line is shown in the figure given below, calculate the maximum velocity of the particle starting from rest in 6 seconds.

a food packet is released from a helicopter which is rising steadily at 2 m/s

after 2 sec ( i ) what is the velocity of the packet ( ii) how far is it below the helicopter?

A particle is in motion along a straight track. As it crosses a fixed point, a stop watch is started. A body travels a distance 180cm in the first 3s and 220cm in the next 5s. What will be it velocity at the end of ninth second?

^{2}=2+t. Its acceleration will be ??????a particle moving along x- axis has acceleration f at time t given by f = fo[1+t / T] where fo and t are constant. the particle at t = 0 has zero velocity .in time interval b/w t = 0 and instant when f=0 the particle velocity vx is

What is the difference between

delta x/delta t and dx/dt ?A car accelerates from rest at a constant rate A for some time after which it retards at constant rate B to come to rest. If the total time lapse is T seconds, evaluate the maximun velocity reached and total distance travelled, in terms of A, B and T

A highway motorist travels at a constant velocity of 45Km /h in a 30Km/h zone . A motor-cyclist police officer has been watching from behind a bill board and at the Same moment the speeding motorist passes the bill board; the police officer accelerates uniformly from rest to overtake her. If the acceleration of the police officer is 10 km h-2 how long does betake to reach the motorist?

The Driver Of A Train Moving At A Speed at V1, sights another train at a distance d, ahead of him moving in the same direction with a slower speed V2. He Applies The Brakes And Gives A Constant retardation a to his train. Show That there will be no collision If d>(V1-V2)*2/2a.

A jet airplane travelling at the speed of 500 km h^{–1}ejects its products of combustion at the speed of 1500 km h^{–1}relative to the jet plane. What is the speed of the latter with respect to an observer on ground?a) a

^{2}= x + 3b) a=2x

^{2}+ 4c) 2a =3x + 5

d) a=4x - 5

if air resistance is to be considered while analysing the motion of a particle thrown vertically upwards, which of the following relationships between time of ascent and time of descent is correct? a. t

_{asc}= t_{des}b. t_{asc}> t_{des}c.t_{asc}< t_{des}d. eiter b or c depending onthe mass of the projectile

How can we derive the distance travelled in nth second by calculus method? Please derive it...

Four particles A,B,C and D are situated at the corners of a square ABCD of side a at t=0.Each particle moves with constant speed v.A always has its velocity along AB, B along BC,C along CD, D along DA. At what time will these particles meet each other?

A car is moving on a straight road covers one third of the distance with a speed of 20 kn/hr and the rest with a speed of 60 km/hr. the average speed of the car is?

^{2}. It reaches a greatest height of 16.53m. Calculate its initial speed.A stone dropped from top of tower is found to travel (5/9) of the height of tower during the last second of its fall. The time of fall is??

a motor car is going due north at a speed of 50 km/h.it makes a 90

^{o}left turn without changin its speed the change in velocity of the car is ?a body moves in a straight line along the x axis . its distance from the origin is given by

x = 8t - 3t

^{2}where x is in meters and t is in seconds . find the displacement of the particle when its velocity is zero.a body moving with uniform retardation covers 3km before the speed is reduced to half of its initial value. It comes to rest in another distance of how many metres?

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A bullet loses 1/20 of its velocity in passing through a plank.What is the least number of planks required to stop the bullet?

^{-1}(3/4), it hits the pole orthogonally 1.5 m below the mark. Find the speed and angle of projection so that it hits the mark orthogonally to the pole. (g = 10 m/s^{2})a car starting from rest accelerates at the rate f through a dist. s, then continues at constant speed for some time and then decelerates at the rate of f/2to come to rest. if the total dist. is 5s., then prove that s=ft

^{2}/2can u tell hw to use natural tangents in logarithmic tables book

A Parachutist bails out from an aeroplaneand after dropping through a distance of 40m opens the parachute and decelerates at 2m/s2 if he reach the ground with a speed of 2m/s how long he is in air? at what height did he bail out from the plane

a) At what times was the point at its starting position?

b) At what times its velocity equal to zero?

A ball projected from ground vertically upward is at same height at time t1 and t2 . the speed of projection of ball is

An Athelete completes one round of a circular track of radius 'R' in 40 seconds. What will be his displacement at the end of 2 minutes 20 seconds ?

Choose the correct answer:

Q.1. The upper curve y = 6x (straight line) and lower curve is y = 3${x}^{2}$ (parabola) as shown in the figure given below. The area lies between the points where those curve intersect is

(1) 1 unit

(2) 2 unit

(3) 3 unit

(4) 4 unit

A car is moving with the Speed of 50 Km/h can be stopped by brakes after at least 6m.What will be the minimum stopping distance, if the same car is moving at the speed of 100 Km/Hr.

The distance x of a particle moving in 1 dimension under the action of a constant force is related to time t by equation t = root over x + 3 where x is in metres and t is in seconds . Find the displacement when it's velocity is zero.

Two trains A and B each of length 100m running on parallel tracks.One overtakes other in 20seconds.One cross other in 10 seconds.Calculate velocity of each train.?

from top of a tower ,a ball is dropped to fall freely under gravity & at the same time, another ball is thrown up with a velocity of 50m/sec. plot the position-time graph for motin of 2 balls during time interval t=0 to t=5 sec. take g=10

a bus is moving with a speed of 10m/s on a straight road. a scooterist wishes to overtake the bus in 100 sec. if the bus is at a distance of 1 k from the scooterist , with what speed the scooterist chase the bus?

two masses in the ratio 1:2 are thrown vertically upwards with same speed.what is the effect on the time by the mass?

A stone is dropped from top of the tower of height

After 1 second another stone is dropped from the balcony 20m below the top." h".Both reach the bottom simultaneously. what is the value of h? taking g=10m/sec

^{2}A body starting from rest accelerates uniformly at the rate of 10cm/s

^{2 }and retards uniformly at the rate of 20 m/s^{2 }. Find the least time in which it can complete the journey of 15km if the maximum velocity attained by the body is 72km/h.The resultant of two forces acting at an angle 150 is 10 kg wt and is perpendicular to one of the forces.The magnitude of smaller force is how much?