Kinematics PYQs Set 11 (PDF)

Set 11 of 14 · Questions 301-330 of 405

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinematics · Set 11 (Q301-330)
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301. $The position vector of a moving body at any instant of time is given as r = (5 t^{2} i - 5 t j) m . The magnitude and direction of velocity at t = 2 s is,$ (1) $515 m / s, making an angle of tan-14 with - ve Y axis$ (2) $515 m / s, making an angle of tan-14 with + ve X axis$ (3) $517 m / s, making an angle of tan-14 with + ve X axis$ (4) $517 m / s, making an angle of tan-14 with - ve Y axis$ 302. $The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance travelled by the body in time 0 to 10s is$ (1) $1:1$ (2) $1:4$ (3) $1:2$ (4) $1:3$ 303. $The position of a particle related to time is given by x = (5 t^{2} -4t+5) m. The magnitude of velocity of the particle at t = 2 s will be :$ (1) $06 m s^{- 1}$ (2) $14 m s^{- 1}$ (3) $10 m s^{- 1}$ (4) $16 m s^{- 1}$ 304. $A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone startsto fall from a point 25 m below the top, Both stones reach the bottom of building simultaneously. The heightof the building is:$ (1) $45 m$ (2) $35 m$ (3) $25 m$ (4) $50 m$ 305. $A ball is dropped from a high-rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v . The two balls meet at t = 18 s . What is the value of v ? (Take g = 10 m / s^{2})$ (1) $75 m / s$ (2) $55 m / s$ (3) $40 m / s$ (4) $60 m / s$ 306. $A missile is fired for maximum range with an initial velocity of 20 m / s . If g = 10 m / s^{2}, the range of the missile is$ (1) $40 m$ (2) $50 m$ (3) $60 m$ (4) $20 m$ 307. $Car A is moving to the East with a speed of 30 km / hr, and car B is moving to the North with the same speed. What is the velocity of car B as measured in car ?$ (1) $42 km / hr, 45 North of West$ (2) $42 km / hr, 45 East of North$ (3) $60 km / hr, 45 South of East$ (4) $42 km / hr, 45 South of East$ 308. $The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by :$ (1) (2) (3) (4) 309. $A body dropped from a height h with initial velocity zero, strikes the ground with a velocity 3 m / s . Another body of same mass dropped from the same height h with an initial velocity of 4 m / s . The final velocity of second mass, with which it strikes the ground is$ (1) $5 m / s$ (2) $12 m / s$ (3) $3 m / s$ (4) $4 m / s$ 310. $The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m /s and due east. If he is standing on the south bank and wishes to cross the river along the shortest path the angle at which he should make his stroke w.r.t. north is given by :-$ (1) $45º west$ (2) $30º west$ (3) $0º$ (4) $60º west$ 311. $An engine of a train, moving with uniform acceleration, passes the signal post with velocity u and the lastcompartment with velocity v . The velocity with which middle point of the train passes the signal post is:$ (1) $\frac{v ^{2} - u ^{2}}{2}$ (2) $\frac{v - u}{2}$ (3) $\frac{v ^{2} + u ^{2}}{2}$ (4) $\frac{u + v}{2}$ 312. $The sum of the magnitudes of two vectors acting at a point is 18 and the magnitude of their resultant is 12 . If the resultant is at 90^{\circ} with the vector of smaller magnitude, then the magnitudes of the vectors are$ (1) $5,13$ (2) $2,16$ (3) $6,12$ (4) $8,10$ 313. $An aircraft is flying at a height of ' H' above the ground and at a speed of ' V . The maximum angle subtended at a ground observation point by the aircraft after time T is$ (1) $tan^{- 1} (\frac{VT}{H})$ (2) $tan^{- 1} (\frac{VT}{2 H})$ (3) $2 tan^{- 1} (\frac{2 VT}{H})$ (4) $2 tan^{- 1} (\frac{VT}{2 H})$ 314. $The position-time graphs for two students A and B returning from the school to their homes are shown in figure. (A) A lives closer to the school (B) B lives closer to the school (C) A takes lesser time to reach home (D) A travels faster than B (E) B travels faster than A Choose the correct answer from the options given below$ (1) $(A) (C) and (D) only$ (2) $(A), (C) and (E) only$ (3) $(B) and (E) only$ (4) $(A) and (E) only$ 315. $The velocity (v) - Distance (x) graph is shown in figure. Which graph represents acceleration (a) versus distance (x) variation of this system?$ (1) (2) (3) (4) 316. $A passenger sitting in a train A moving at 90 km h^{- 1} observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km h^{- 1}, then length of train B is:$ (1) $120m$ (2) $320m$ (3) $80m$ (4) $200m$ 317. $A particle moving in a straight line covers half the distance with speed 6 m / s . The other half is covered in two equal time intervals with speeds 9 m / s and 15 m / s respectively. The average speed of the particle during the motion is :$ (1) $10 m / s$ (2) $8 m / s$ (3) $9.2 m / s$ (4) $8.8 m / s$ 318. $A butterfly is flying with a velocity 42 m / s in North-East direction. Wind is slowly blowing at 1m/s from North to South. The resultant displacement of the butterfly in 3 seconds is :$ (1) $3m$ (2) $20m$ (3) $122 m$ (4) $15m$ 319. $If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?$ (1) (2) (3) (4) 320. $The displacement of a body when it covers a distance of C /4 (where, C is circumference along the circumference of the circle of radius r with a uniform speed u is)$ (1) $r$ (2) $r 2$ (3) $2 r$ (4) $\frac{r}{2}$ 321. $For a body moving along a straight line, the following v - t graph is obtained. According to the graph, the displacement during$ (1) $uniform acceleration is greater than that during uniform motion.$ (2) $uniform acceleration is less than that during uniform motion.$ (3) $uniform acceleration is equal to that during uniform motion.$ (4) $uniform motion is zero.$ 322. $An ant starts from the origin and crawls 10 cm along the x -axis and then 20 cm along the y -axis. The dot product of the ant's displacement vector with the position vector of a point that makes 45^{\circ} with the x-axis and has a magnitude of 2 cm is$ (1) $30 cm$ (2) $302 cm$ (3) $\frac{30}{2} cm$ (4) $15 cm$ 323. $A particle starts from the origin at time t = 0 and moves along the positive x -axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5 s ?$ (1) $10 m$ (2) $6 m$ (3) $3 m$ (4) $9 m$ 324. $An airplane flies 400 m north and 300 m south and flies 1200 m upward, then net displacement is$ (1) $1400 m$ (2) $1500 m$ (3) $1200 m$ (4) $1100 m$ 325. $A particle moves along a straight line along the x -axis. Its position (x) versus time () graph is shown in the figure [x in meters and t in seconds]. It's average speed during this motion is$ (1) $0.4 ms^{- 1}$ (2) $1.0 ms^{- 1}$ (3) $0.8 ms^{- 1}$ (4) $0.6 ms^{- 1}$ 326. $A particle starts with an initial velocity of 10.0 m s^{- 1} along x-direction and accelerates uniformly at the rate of 2. 0 m s^{- 2} . The time taken by the particle to reach the velocity of 60. 0 m s^{- 1} is_____.$ (1) $25s$ (2) $3s$ (3) $6s$ (4) $30s$ 327. $The instantaneous velocity of a particle moving in a straight line is given as v = α t + β t^{2}, where α and β are constants. The distance travelled by the particle between 1s and 2s is :$ (1) $3 α + 7 β$ (2) $\frac{3}{2} α + \frac{7}{3} β$ (3) $\frac{α}{2} + \frac{β}{3}$ (4) $\frac{3}{2} α + \frac{7}{2} β$ 328. $A tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height \frac{h}{2} The velocity versus height of the ball during its motion may be represented graphically by (graph are drawn schematically and on not to scale)$ (1) (2) (3) (4) 329. $A bob of mass M is suspended by a massless string of length L . The horizontal velocity V at position A is just sufficient to make it reach the point B . The angle θ at which the speed of the bob is half of that at A, satisfies. Figure:$ (1) $θ = \frac{π}{4}$ (2) $\frac{π}{4} < θ < \frac{π}{2}$ (3) $\frac{π}{2} < θ < \frac{3 π}{4}$ (4) $\frac{3 π}{4} < θ < π$ 330. $A river is flowing from west to east direction with speed of 9 km h^{- 1} . If a boat capable of moving at a maximum speed of 27 km h^{- 1} in still water, crosses the river in half a minute, while moving with maximum speed at an angle of 150^{\circ} to direction of river flow, then the width of the river is:$ (1) $112.5 m$ (2) $75 m$ (3) $300 m$ (4) $112.5 \times 3 m$