Kinematics PYQs Set 1 (PDF)

Set 1 of 14 · Questions 1-30 of 405

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinematics · Set 1 (Q1-30)
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1. $A river has a steady speed of ' v'. A man swims upstream at a distance of 'd' and swims back to the starting point in total time ' t'. The man can swim at a speed of ' 2 v' in still water. If the time taken by the man in still water is ' t_{0}' to complete the same length of swim, then \frac{t}{t _{0}} is$ (1) $\frac{1}{2}$ (2) $\frac{3}{2}$ (3) $\frac{3}{4}$ (4) $\frac{4}{3}$ 2. $Velocity (v) and acceleration (a) in two systems of n units 1 and 2 are related as v_{2} = \frac{n}{m ^{2}} v_{1}, and a_{2} = \frac{a _{1}}{mn} respectively. Here m and n are constants. The relations for distance and time in two systems respectively are:$ (1) $\frac{n ^{3}}{m ^{3}} L_{1} = L_{2} and \frac{n ^{2}}{m} T_{1} = T_{2}$ (2) $L_{1} = \frac{n ^{4}}{m ^{2}} L_{2} and T_{1} = \frac{n ^{2}}{m} T_{2}$ (3) $L_{1} = \frac{n ^{2}}{m} L_{2} and T_{1} = \frac{n ^{4}}{m ^{2}} T_{2}$ (4) $\frac{n ^{2}}{m} L_{1} = L_{2} and \frac{n ^{4}}{m ^{2}} T_{1} = T_{2}$ 3. $Two guns A and B can fire bullets at speeds 1 km / s and 2 km / s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:$ (1) $1 : 16$ (2) $1 : 2$ (3) $1 : 4$ (4) $1 : 8$ 4. $A car moving with a velocity of 20 m s^{- 1} is stopped in a distance of 40 m . If the same car is travelling at double the velocity, the distance travelled by it for same retardation is$ (1) $640 m$ (2) $320 m$ (3) $1280 m$ (4) $160 m$ 5. $The speed of a particle changes from 5 ms^{- 1} to 25 ms^{- 1} in a time t . If the magnitude of change in its velocity is 5 ms^{- 1}, the angle between the initial and final velocities of the particle is$ (1) $30^{\circ}$ (2) $45^{\circ}$ (3) $60^{\circ}$ (4) $90^{\circ}$ 6. $Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t_{1} . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t_{2} . The time taken by her to walk up on the moving escalator will be :$ (1) $\frac{t _{1} + t _{2}}{2}$ (2) $\frac{t _{1} t _{2}}{t _{2} - t _{1}}$ (3) $\frac{t _{1} t _{2}}{t _{2} + t _{1}}$ (4) $t_{1} - t_{2}$ 7. $A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two ball meet at t = 18s. What is the value of v? [take g = 10 m s^{-2}]$ (1) $75 m s^{-1}$ (2) $55 m s^{-1}$ (3) $40 m s^{-1}$ (4) $60 m s^{-1}$ 8. $Two particles are projected from the same point with the same speed u such that they have the same range R but different maximum heights, h_{1} and h_{2} Which of the following is correct?$ (1) $R^{2} = 4 h_{1} h_{2}$ (2) $R^{2} = 16 h_{1} h_{2}$ (3) $R^{2} = 2 h_{1} h_{2}$ (4) $R^{2} = h_{1} h_{2}$ 9. $A projectile is given an initial velocity of i + 2 j ms^{- 1} . The cartesian equation of its path is (x and y are in metres and g = 10 ms^{- 1})$ (1) $y = x - 5 x^{2}$ (2) $y = 2 x - 5 x^{2}$ (3) $y = 2 x - 15 x^{2}$ (4) $y = 2 x - 25 x^{2}$ 10. $Two projectiles are fired from ground with same initial speeds from same point at angles (45^{\circ} +) α) and (45^{\circ} - α) with horizontal direction. The ratio of their times of flights is$ (1) $\frac{1 + tan α}{1 - tan α}$ (2) $\frac{1 + sin 2 α}{1 - sin 2 α}$ (3) $\frac{1 - tan α}{1 + tan α}$ (4) $1$ 11. $The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectiles is:$ (1) $θ = t a n^{-1}$ (2) $θ = t a n^{-1} (4)$ (3) $θ = t a n^{-1} (2)$ (4) $θ = 45º$ 12. $A car travels in a straight line along a road. Its distance x from a stop sign is given as a function of t by the equation x (t) = αt + β t^{3}, where α = 2.0 m / s, β = 0.01 m / s^{3} . Calculate the average velocity of the car in the time interval t = 2.00 s to 4.00 s .$ (1) $2.28 m / s$ (2) $4.94 m / s$ (3) $3.34 m / s$ (4) $4.12 m / s$ 13. $If the velocity of a particle moving along a straight line with uniform acceleration, is given by V = (196 - 16 X) ms^{- 1}, then its acceleration is (x is displacement of the particle)$ (1) $8 ms^{- 2}$ (2) $14 ms^{- 2}$ (3) $- 8 ms^{- 2}$ (4) $- 16 ms^{- 2}$ 14. $A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with 3 m / s^{2} . At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m / s - The initial height of the airplane is____m. (g = 10 m / s^{2})$ (1) $82.5$ (2) $20$ (3) $62.5$ (4) $92.5$ 15. $A ball is projected from the ground with a speed 15 m s^{- 1} at an angle θ with horizontal so that its range and maximum height are equal, then 'tan θ' will be equal to$ (1) $\frac{1}{4}$ (2) $\frac{1}{2}$ (3) $2$ (4) $4$ 16. $A body starts from rest and moves with constant acceleration for ts . It travels a distance x_{1} in first half of time and x_{2} in next half of time, then$ (1) $x_{2} = 3 x_{1}$ (2) $x_{2} = x_{1}$ (3) $x_{2} = 4 x_{1}$ (4) $x_{2} = 2 x_{1}$ 17. $A rocket lifts off from ground and accelerate upwards at 1 ms^{- 2} 20 s after, lift off a piece breaks off from the bottom of rocket. After breaking off, how much time it takes approximately to reach the ground? (Take g = 10 ms^{- 2})$ (1) $6.3 s$ (2) $4.5 s$ (3) $10.5 s$ (4) $8.5 s$ 18. $If A = 2 i + 3 j + 8 k is perpendicular to B = 4 j - 4 i + α k, then the value of ' α' is$ (1) $1$ (2) $\frac{1}{2}$ (3) $-1$ (4) $- \frac{1}{2}$ 19. $A particle moves along the x -axis and has its displacement x varying with time t according to the equation: x = c_{0} (t^{2} - 2) + c (t - 2)^{2} where c_{0} and c are constants of appropriate dimensions. Then, which of the following statements is correct?$ (1) $the acceleration of the particle is 2 (c + c_{0})$ (2) $the acceleration of the particle is 2 c_{0}$ (3) $the acceleration of the particle is 2 c$ (4) $the initial velocity of the particle is 4 c$ 20. $A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is$ (1) $10 m / s, 0$ (2) $0, 0$ (3) $0, 10 m / s$ (4) $10 m / s, 10 m / s .$ 21. $The motion of a particle along a straight line is described by equation: x = 8 + 12 t - t^{3} where x is in meter and t in second. The retardation of the particle when its velocity becomes zero, is:$ (1) $24 m s^{-2}$ (2) $zero$ (3) $6 m s^{-2}$ (4) $12 m s^{-2}$ 22. $A train of 150 metre length is going towards north direction at a speed of 10 m / s . A parrot flies at the speed of 5 m / s towards south direction parallel to the railways track. The time taken by the parrot to cross the train is$ (1) $12 sec$ (2) $8 sec$ (3) $15 sec$ (4) $10 sec.$ 23. $The velocity of a particle is given by v = 2 t^{2} - 8 t + 15 ms^{- 1} . Find its instantaneous acceleration at t = 5 s .$ (1) $18 ms^{- 2}$ (2) $20 ms^{- 2}$ (3) $5 ms^{- 2}$ (4) $12 ms^{- 2}$ 24. $A car starts from rest and accelerates at 5 m / s^{2} . At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s ? (Take, g = 10 m / s^{2}) [NEET 2021]$ (1) $202 m / s, 10 m / s^{2}$ (2) $20 m / s, 5 m / s^{2}$ (3) $20 m / s, 0$ (4) $202 m / s, 0$ 25. $A particle starts from the origin at t = 0 with an initial velocity of 3.0 i^m / s and moves in the x - y plane with a constant acceleration (6.0 i^+ 4.0 j^) m / s^{2} The x -coordinate of the particle at the instant when its y -coordinate is 32 m is D meters. The value of D is:$ (1) $50$ (2) $40$ (3) $32$ (4) $60$ 26. $At any instant ' I' the vertical distance ' Y' and horizontal distance ' X' of a projectile are given by 2 Y = 6 t - gt^{2} and X = 4 t . The initial velocity of projectile is (X and Y are in metre and t is in second)$ (1) $3 ms^{- 1}$ (2) $4 ms^{- 1}$ (3) $5 ms^{- 1}$ (4) $6 ms^{- 1}$ 27. $A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t_{1} . If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t_{2} . Time required to reach the ground, if it is dropped from the top of the tower, is :$ (1) $t_{1} t_{2}$ (2) $t_{1} + t_{2}$ (3) $t_{1} - t_{2}$ (4) $\frac{t _{1}}{t _{2}}$ 28. $A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle θ to the horizontal, the maximum height attained by it is equal to 4 R . The angle of projection θ is then given by :$ (1) $sin^{- 1} (\frac{2 gT ^{2}}{π ^{2} R})^{\frac{1}{2}}$ (2) $sin^{- 1} (\frac{π ^{2} R}{2 gT ^{2}})^{\frac{1}{2}}$ (3) $cos^{- 1} (\frac{2 gT ^{2}}{π ^{2} R})^{\frac{1}{2}}$ (4) $cos^{- 1} (\frac{π R}{2 gT ^{2}})^{\frac{1}{2}}$ 29. $A body starts moving from rest with constant acceleration covers displacement S_{1} in first (p - 1) seconds and S_{2} in first p seconds. The displacement S_{1} + S_{2} will be made in time :$ (1) $(2 p + 1) s$ (2) $(2 p^{2} - 2 p + 1) s$ (3) $(2 p - 1) s$ (4) $(2 p^{2} - 2 p + 1) s$ 30. $A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is \frac{1}{x} . The value of x is_____.$