Kinematics PYQs Set 10 (PDF)

Set 10 of 14 · Questions 271-300 of 405

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinematics · Set 10 (Q271-300)
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271. $A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = F_{0} e^{- b t} in the x direction. Its speed v(t) is depicted by which of the following curves?$ (1) (2) (3) (4) 272. $A person walks in such a way that he covers equal distance in each step. The person takes 2 steps forward towards east, then takes a right turn and walks 4 steps towards south, then takes a right turn and walks 6 steps towards west and then takes a right turn and walks further. The direction of his final position after a total of 20 steps walk with respect to his initial position is$ (1) $North-West$ (2) $60^{\circ} West of South$ (3) $60^{\circ} South of West$ (4) $South-East$ 273. $A rubber ball is dropped from a height of 5 m on a plane. On bouncing it rises to 1.8 m . The ball loses its velocity on bouncing by a factor of$ (1) $\frac{3}{5}$ (2) $\frac{2}{5}$ (3) $\frac{16}{25}$ 274. $A projectile is fired at an angle of 45º with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection is:$ (1) $60º$ (2) $tan^{- 1} (\frac{1}{2})$ (3) $tan^{- 1} (\frac{3}{2})$ (4) $45º$ 275. $The velocity-displacement graph describing the motion of a bicycle is shown in the figure. The acceleration-displacement graph of the bicycle's motion is best described by:$ (1) (2) (3) (4) 276. $A particle starts from a (m s^{- 2}) rest. Its acceleration a versus time t is shown in the figure. The maximum speed of the particle will be$ (1) $80 m s^{- 1}$ (2) $40 m s^{- 1}$ (3) $18 m s^{- 1}$ (4) $2 m s^{- 1}$ 277. $A scooter accelerates from rest for time t_{1} at constant rate a_{1} and then retards at constant rate a_{2} for time t_{2} and comes to rest. The correct value of \frac{t _{1}}{t _{2}} will be:$ (1) $\frac{a _{1} + a _{2}}{a _{2}}$ (2) $\frac{a _{2}}{a _{1}}$ (3) $\frac{a _{1} + a _{2}}{a _{1}}$ (4) $\frac{a _{1}}{a _{2}}$ 278. $Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m with the same velocity of 25 m / s . When and where will the two bullets collides. (g = 10 m / s^{2}) [NEET 2019]$ (1) $After 2 s at a height 180 m$ (2) $After 2 s at a height of 20 m$ (3) $After 4 s at a height of 120 m$ (4) $They will not collide$ 279. $Two cars are travelling towards each other at speed of 20 m s^{- 1} each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s^{- 2} . The distance between them when they come to rest is:$ (1) $200 m$ (2) $100 m$ (3) $50 m$ (4) $25 m$ 280. $Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in m s^{- 1} . [use g = 10 m s^{- 2}] :$ (1) $10$ (2) $15$ (3) $20$ (4) $30$ 281. $A particle moves along a straight line O X . At a time t (in seconds) the distance x (in metres) of the particle fr om O is given by x = 40 + 12 t - t^{3} . How long would the particle travel before coming to rest?$ (1) $16 m$ (2) $24 m$ (3) $40 m$ (4) $56 m$ 282. $A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be$ (1) $150 m / s$ (2) $75 m / s$ (3) $37.5 m / s$ (4) $45 m / s$ 283. $A projectile is launched from point A of the given landscape with a water body as shown in the diagram. The launching angle is 15^{\circ} . From the following, identify the right initial velocity of the projectile with which it will fall somewhere in between the points C and D . [Assume, g = 10 m / s^{2}]$ (1) $21.5 m / s$ (2) $22.5 m / s$ (3) $19.5 m / s$ (4) $24.0 m / s$ 284. $Two objects are projected with same velocity 'u' however at different angles α and β with the horizontal. If α + β = 90°, the ratio of horizontal range of the first object to the 2^{n d} object will be :$ (1) $4: 1$ (2) $2: 1$ (3) $1 : 2$ (4) $1 : 1$ 285. $A ball is spun with angular acceleration α = 6 t^{2} - 2 t where t is in second and a is in r a d s^{- 1} . At t =0, the ball has angular velocity of 10 r a d s^{- 1} and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:$ (1) $\frac{3}{2} t^{4} - t^{2} + 10 t$ (2) $\frac{t ^{4}}{2} - \frac{t ^{3}}{3} + 10 t + 4$ (3) $\frac{2 t ^{4}}{3} - \frac{t ^{3}}{6} + 10 t + 12$ (4) $2 t^{4} - \frac{t ^{3}}{2} + 5 t + 4$ 286. $The displacement-time graphs of two moving particles make angles of 30^{\circ} and 45^{\circ} with the time axis. The ratio of their velocities is$ (1) $3 : 2$ (2) $1 : 1$ (3) $1 : 2$ (4) $1 : 3$ 287. $The vector sum of two forces is perpendicular to their vector differences. In that case, the forces$ (1) $are equal to each other$ (2) $are equal to each other in magnitude$ (3) $are not equal to each other in magnitude$ (4) $cannot be predicted.$ 288. $A particle is thrown vertically upward. Its velocity at half of the height is 10 m / s, then the maximum height attained by it (g = 10 m / s^{2})$ (1) $8 m$ (2) $20 m$ (3) $10 m$ (4) $16 m$ 289. $Assertion (A) : The velocity of a projectile at a point on its trajectory is equal to the slope at that point. Reason (R) : The velocity vector at a point always along the tangent to the trajectory at that point.$ (1) $Both A and R are true and R is the correct explanation of A$ (2) $Both A and R are true but R is not the correct explanation of A$ (3) $A is true but R is false$ (4) $A is false but R is true$ 290. $A shot is fired from a point at a distance of 200 m, from the foot of a tower 100 m high, so that it just passes over it. The direction of shot with respect to the horizontal is$ (1) $30^{\circ}$ (2) $60^{\circ}$ (3) $70^{\circ}$ (4) $45^{\circ}$ 291. $A bus is moving with a s peed of 10 m s^{- 1} o na straight road. A scooterist wishes to overtake the bus in 100 s . If the bus is at adistance of 1 km from the scooterist, with what speed should the scooterist chase the bus?$ (1) $40 m s^{- 1}$ (2) $25 m s^{- 1}$ (3) $10 m s^{- 1}$ (4) $20 m s^{- 1}$ 292. $If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is$ (1) $4 5^{o}$ (2) $18 0^{o}$ (3) $0^{o}$ (4) $9 0^{o}$ 293. $A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching \frac{h}{3} in both the directions.$ (1) $\frac{2 - 1}{2 + 1}$ (2) $\frac{1}{3}$ (3) $\frac{3 - 2}{3 + 2}$ (4) $\frac{3 - 1}{3 + 1}$ 294. $Motion of a particle is given by equation s = (3 t^{3} + 7 t^{2} + 14 t + 8) m . The value of acceleration of the particle at t = 1 sec is$ (1) $10 m / s^{2}$ (2) $32 m / s^{2}$ (3) $23 m / s^{2}$ (4) $16 m / s^{2}$ 295. $A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time? (Given g = 9.8 m / s^{2})$ (1) $more than 19.6 m / s$ (2) $at least 9.8 m / s$ (3) $any speed less than 19.6 m / s$ (4) $only with speed 19.6 m / s$ 296. $A body is moving along a straight line with initial velocity v_{0} . Its acceleration a is constant. After t seconds, its velocity becomes v . The average velocity of the body over the given time interval is$ (1) $v = \frac{v ^{2} - v _{0}^{2}}{at}$ (2) $v = \frac{v ^{2} + v _{0}^{2}}{2 at}$ (3) $v = \frac{v ^{2} + v _{0}^{2}}{at}$ (4) $v = \frac{v ^{2} - v _{0}^{2}}{2 at}$ 297. $For a projectile motion, the angle between the velocity and acceleration is minimum and acute at$ (1) $only one point$ (2) $two points$ (3) $three points$ (4) $four points.$ 298. $Ball-1 is dropped from the top of a building from rest. At the same moment, ball-2 is thrown upward towards ball1 with a speed 14 m / s from a point 21 m below the top of building. How far will the ball-1 have dropped when it passes ball-2. (Assume acceleration due to gravity, g = 10 m / s^{2} .)$ (1) $\frac{45}{4} m$ (2) $\frac{52}{6} m$ (3) $\frac{37}{2} m$ (4) $\frac{25}{2} m$ 299. $A swimmer can swim with velocity of 12 km / h in still water. Water flowing in a river has velocity 6 km / h . The direction with respect to the direction of flow of river water he should swim in order to reach the point onthe other bank just opposite to his starting point is___ (Round off to the Nearest Integer) (find the angle indegree)$ 300. $A horse rider covers half the distance with 5 m/s speed The remaining part of the distance was travelled with speed 10 m/s for half the time and with speed 15 m/s for other half of the time. The mean speed of the rider averaged over the whole time of motion is x/7 m/s. The value of x is$