Kinematics Questions and Answers

19 A man running on a horizontal road at 8 km h finds the rain falling vertically He increases his speed to 12 km h and finds that the drops make angle 30 with the vertical Find the speed and direction of the rain with respect to the road

zontally with velocity v from a building of height h It hits the inclined plane perpendicularly as shown in figure Then hi 1 Time taken to hit the plane is 2 Time taken to hit the plane is 3 The value of v is gh V2 cot a 2ah V g tana v tan a g

2kg HA 0 3 3m A plank of mass 10kg rests on a smooth horizontal surface Two blocks A and B of masses mA 2 kg and MB 1 kg lies at a distance of 3 m on the plank as shown in the figure The friction coefficient between the blocks and plank are A 0 3 and g 0 1 Now a force F 15 N is applied to the plank in horizontal direction Find the time in sec after which block A collides with B M 10kg F p 0 A 10 B MB 0 1

Speed time graph of two cars A B approaching towards each other is shown in figure Initial distance between them is 60m The cars will cross each other after time 20 v m s a 2 sec c 1 5 sec 2 4 t s b 3sec d 2 sec

takes 5 steps forward and 3 steps backward and so A drunkard is walking along a straight road on the road 11 m away from the starting point The on Each step is 1 m long and takes 1 s There is a pit drunkard will fall into the pit after a 21 s b 29 s c 31 s d 37 s

27 A body is moving towards north with initial velocity of 13 ms 1 It is subjected to a retardation of 2 ms 2 towards south The distance travelled by it in 7th second is 1 Zero 3 0 25 m 2 0 75 m 4 0 5 m

3 A projectile is projected in a plane from origin with initial velocity u U U If acceleration due to gravity is taken along then maximum displacement in x direction would be 1 2 20 42 g 44 42 2 15N FN

A particle move with velocity v for time t and v for time t along a straight line The magnitude of its average acceleration is V V 2 1 1 1 3 V V t t 2 4 V V t t V V 2 t t

A falling particle in the last second of its fall passes through 58 86 m Total time of fall is 2 6 5 s 4 8 5 s 1 5 5 s 3 7 5 s

2 3 given as x t a sinot and y t a sin2wt Its trajectory will look like 1 y D y y y X x x

The speed of a projectile at its maximum height is half of its initial speed The angle of projection is 1 15 2 30 3 45 4 60

The displacement x time t graph of a particle is shown in figure Which of the following is correct 9 X of a Particle starts with zero velocity and variable acceleration b Particle starts with non zero velocity and variable acceleration c Particle starts with zero velocity and uniform acceleration d Particle starts with non zero velocity and uniform acceleration t

1 The equation of motion of a particle moving along a straight line is given by s 63 t 6t t cm Find its velocity after 2 s and the distance covered by it before coming to rest 27 cm 108 cm

3 A body moves along a straight line with uniform acceleration and at instants t 0 1 2 3 s it is at distances of 30 52 5 80 and 112 5 m from a fixed point Find its acceleration and velocity at t 0 5 m s 20 m s CiaW At what

A particle of mass 10 2 kg under the action of a force k F x 2x is in motion along the positive x direc tion At time t 0 the position of the particle is x 1 0 m and velocity 0 If k 10 2 N m i find the velocity when the particle is at x 0 50 m ii When will the particle be in the position x 0 25 m Ans i 1m s 1 ii 1 479 s

A string wound around a solid cylinder is unwound by applying a force of 20 N Calculate the torque acting on the cylinder and angular acceleration produced in the cylinder of mass 2 5 kg and of radius 50 cm 10 N m 32 rad s 21

the weight up In the figure shown all surfaces are smooth and block A and wedge B have mass 10 kg and 20 kg respectively Find normal reaction between block A B spring force and normal reaction of ground on block B g 10 m s Find the reading of the massless spring balance in the given condition 10 137 20

LEVEL I If a car moves with velocity v and its maximum retardation is a its minimum stopping distance proportional to 1 v 2 v 3 v 4 v1 2

1 16m The displacement x of a body in motion is given by x a sin oot 0 The time at which the displacement is maximum is 1 2 TC 0 20 3 TU 20 4 2 0

219 A particle starts from 1 0 in the x y plane along a straight path making an angle of 60 with the x axis Which of the following will not be the coordinate through which the particles will pass 1 0 3 2 1 2 3

3 b ln 1 4b The velocity time 4 b relation of a body starting from m 2 S4 rest is given by v k 3 2 where K The distance traversed in 4 seconds is 2 1 2 00 m 3 25 6 m 2 2 56 m 4 256 m niyen by relati

P 4 A stone dropped from the top of a tower of height 300 m high splashes into the water of a pond near the base the tower When is the splash heard at the top given that the speed of sound in air is 340 ms g 9 8 ms 0 87 TORT

33 A body is thrown vertically upwards and takes 5 seconds to reach maximum height The distance travelled by the body will be same in 1 1st and 10th second 2 2nd and 8th second 3 4th and 6th second 4 Both 2 3

Nitika is getting late and so she drives her car in high speed Suddenly she crossing the road She immediately applies brakes and saves the child a What happens when we apply brakes b What can we learn from Nitika a small child Value Corner

4 The position of a particle along x axis at time t is given by x 1 t f The distance travelled by the particle in first 2 seconds is 1 1 m 3 25 m 2 2 m 4 3 m

2 Smooth surface If m m 1 kg then find out distance travelled by m in first 1 0 650 m 0 75 2 m sec 2 0 625 m

Graph of displacement x vs time f is given below for a particle moving in one dimensional motion The velocity time graph for this case would be 1 2 3 20 10 4 2 2 4 1 1 2 Tof 5 10 15 20 5 10 15 20 5 10 15 20 t 5 10 15 20 t t

40 For a body moving with uniform acceleration along straight line the variation of its velocity v with position x is best represented by 1 3 X 2 4 X X

A steamer moves towards north with a velocity v Smoke from the chimney comes out at 30 towards south with respect to the east If wind is blowing from the west find the speed of the wind 1 3v1

Two cars are moving in the same direction at the same speed u The cars maintained a constant distance x between them An another car third car coming from opposite direction meets the two cars at an interval of t Then find the speed of the thirc car X 1 tu 101 X 2 4 x X U

A particle moves along x axis in such a way that its x co ordinate varies with time according to the equation x 4 2t f2 The speed of the particle will vary with time as 24 it 22V 1 t C M t 3 V O 2 A V V 4 O J t

44 A body is moving with 20 m s towards east After 5 s its velocity becomes 30 m s towards north and continues Then ratio of magnitude of average velocity between 0 to 10 s and average acceleration between 0 to 10 s is 1 7 2 1 3 5 2 13 2 3 4 5 13

4 A man tries to cross the river and reach point B on the opposite bank of river as shown Then the minimum speed relative to water and direction of swimmer at O so that he can reach point B is given river speed is u B 1 1 2 1 30 120 with direction of river flow 2 1 1 0 60 with direction of river flow 2u 3 60 with direction of river flow 3 2u 4 24 120 with direction of river flow To

A compartment gets detached from a train and comes to rest with a constant retardation During this period the train moves with a uniform velocity Prove that the distance traveled by the detached compartment and its distance from the train when it comes to rest are equal ois to each other

The acceleration of an object starting from rest is related to time as a Kt c What will be its velocity after time t Kt ct

Draw position time graphs of two objects moving along a straight line when their relative velocity is zero i non zero Refer to Art 6 23

A particle starting from rest is in uniform acceleration Its displacement in P 1 seconds and P seconds are 1 S and 2 respectively Then what would be its dis placement in the P2 P 1 th second biriq ov UPSEE 06 S S

64 4 None of these A point moves such that its displacement as a function of time is given by x 1 Its acceleration as a function of time t will be 1 2 3 5 X 3 2t 4 X 2 4 2t 5 x 2 5 x

2 Given that a body falling freely passes through 5390 cm in the sixth second Find the value of g 1 1000 cm s 3 950 cm s 2 900 cm s 4 980 cm s

2 A car starting from rest accelerates at the rate f through a distance S then continues at constant speed for time t and f then decelerates at the rate to come to rest If the total 2 distance traversed is 15 S then 2005 a S A 1 6 1 c S 82 4 b S ft d S fi 72

A boat and a motor launch start their journeys from the same point making an angle a between their direc tions of motion Velocity of the launch is m times the velocity of the boat The direction of motion of the launch appears to be at an angle of 45 to a passenger of the boat Prove that sin2a m 1 m 1

A ball is held at rest in position A as shown in the figure by two light cords The horizontal cord is cut and the ball swings as a pendulum What is the ratio of the tensions in the supporting cord in position A to that in position B A 0 0 B

Position time graph for a particle is shown in figure Starting from t 0 at what time t the average velocity is zero 098765432 x m 10 1 0 1 1 s 2 3 s 3 6 s t s 1 2 3 4 5 6 7 8 9 10 11 12 13

An object moving with a constant acceleration a trav els a distance x in time t and distance y in the next time interval t Prove that a 2 2 t t nera

A motor boat set out at 11 a m from a position 61 2j and travels at a steady speed of magnitude 53 on a direct course to intercept a ship The ship maintains a steady velocity vector 3i 4j and at 12 noon is at a position 3i j Find a the velocity vector of the motor boat b the time of interception and c the position vector of point of interception If distances are measured in kilometres and speeds in kilometres per hour

If for a projectile the velocity of projection is u range R time of flight T and maximum height attained H show that g2T4 4T2u 4 R and 16gH4 8u H gr 0 0

28 The reading of spring balance for the system as shown in figure is g 10 m s 44 F 10 N 2 1 3 350 7 175 7 3 kg 0 5 N N L 2 4 4 kg 250 7 500 7 N N F 50 N smooth 1

standing 1 foot away from a wall The balloon reached a maximum height of 64 feet and then hit the ground 17 feet away from the wall Create a table of values to represent the scenario Be Create a graph to represent the scenario The graph sure to include at least five values Values should should include at least the x and y intercepts and the include at least x and y intercepts and the vertex vertex X Identify how you see the x and y intercepts and vertex in the table graph and equation Hint You may want to rewrite the equations in equivalent forms How do you see the x intercepts in the i see it easy Graph 65 60 55 50 45 40 35 30 25 20 15 G T 8 V

The motion of a short distance runner is captured using a motion detector and displayed on the graph shown Use the graph to answer the following questions Right is defined as positive Answers have an 8 tolerance to allow for estimation Describe the runner s direction of travel left Describe the runner s motion increasing speed What is the distance traveled 63 m V What is the final speed m s V What is the magnitude of the acceleration 0 167 m s velocity m s 6 4 2 0 2 4 6 3 6 9 12 15 18 time

p mu KE mv Ellastic Collision 7 FXF T rF sind r F rFL 2nr G 6 674 x 10 11 N m kg T Gm m F 2 vo 0 Ac Part a GM R Problem 1 a Part a refers to the figure on the left A ball is fired with an initial speed 200 m sec at an angle with the horizontal The ball then hits a target that is a distance of 1800 m to the right There are 2 possible values for What are these 2 values for 0 Hint The Trig identity sec 0 1 tan 0 will be helpful You should end up with the quadratic equation a tan 0 btan 0 c 0 where a b and care constants which you can solve for 0 b Part b refers to the figure on the right A ball is fired with an initial speed vo 200 m sec at an angle with the horizontal The ball then hits a target on a slope that makes an angle of 20 with the horizontal The slope starts at a distance of 500 m to the right of where the ball was launched and the target is a distance of 1300 m up the slope There are 2 possible values for 0 What are these 2 values for 8 Hint The Trig identity sec 0 1 tan 0 will be helpful You should end up with the quadratic equation a tan b tan 0 c 0 where a b and c are constants which you can solve for 8 1800 m Vesc Target 2GM R Vo 0 500 m Part b 1300 m 20 Target