Kinematics PYQs Set 2 (PDF)

Set 2 of 12 · Questions 31-60 of 359

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Mere Teacher · Previous Year Questions NEET Physics · Kinematics · Set 2 (Q31-60)
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31. $A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. the ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite directions is :$ (1) $\frac{25}{11}$ (2) $\frac{3}{2}$ (3) $\frac{5}{2}$ (4) $\frac{11}{5}$ 32. $Two position vectors are given by r_{1} = (1, 1, 1) and r_{2} = (1, - 1, 1) . The unit vector in the direction of r_{1} \times r_{2}$ (1) $\frac{i}{2} - \frac{k}{2}$ (2) $- \frac{i}{2} - \frac{k}{2}$ (3) $\frac{i}{2} + \frac{k}{2}$ (4) $- \frac{i}{2} + \frac{k}{2}$ 33. $The maximum height attained by a projectile when thrown at an angle θ with the horizontal is found to be half the horizontal range. Then θ =$ (1) $tan^{- 1} (2)$ (2) $π /6$ (3) $π /4$ (4) $tan^{- 1} (1/2)$ 34. $A projectile is thrown in the upward direction making an angle of 60^{\circ} with the horizontal with a velocity of 140 ms^{- 1} . Then the time after which its velocity makes an angle 45^{\circ} with the horizontal is (Acceleration due to gravity, g = 10 ms^{- 2})$ (1) $0.5124 s$ (2) $51.24 s$ (3) $5.124 s$ (4) $512.4 s$ 35. $If a car at rest accelerates uniformly to a speed of 144 k m / h in 20 sec, it covers a distance of$ (1) $1440 cm$ (2) $2980 cm$ (3) $20 m$ (4) $400 m$ 36. $A particle is moving with a velocity v = K (y i + x j) where K is a constant. The general equation for its path is:$ (1) $y = x^{2} + constant$ (2) $y^{2} = x + constant$ (3) $y^{2} = x^{2} + constant$ (4) $xy = constant$ 37. $A particle has initial velocity (2 i + 3 j) and acceleration (0.3 i + 0.2 j) . The magnitude of velocity after 10 seconds will be :$ (1) $92 units$ (2) $52 units$ (3) $5 units$ (4) $9 units$ 38. $The dot product of unit vectors n_{1} and n_{2} that are parallel to 5 i + 12 j and 3 i + 4 j respectively is$ (1) $\frac{63}{65}$ (2) $63$ (3) $\frac{63}{4225}$ (4) $\frac{63}{845}$ 39. $If the engine of a long train moving with constant acceleration crosses a tree with velocity ' u' and the last compartment of the train crosses the same tree with velocity ' v', then the velocity with which the middle compartment crosses the same tree is$ (1) $\frac{( v + u )}{2}$ (2) $\frac{2 uv}{( u + v )}$ (3) $\frac{( v ^{2} + u ^{2} )}{2}$ (4) $2 (u^{2} + v^{2})$ 40. $Two cars P and Q start from a point at the same time in a straight line and their positions are represented by X_{P} (t) = at + b t^{2} and X_{Q} (t) = ft - t^{2} . At what time do the cars have the same velocity? [NEET 2016]$ (1) $\frac{a - f}{1 + b}$ (2) $\frac{a + f}{2 ( b - 1 )}$ (3) $\frac{a + f}{2 ( 1 + b )}$ (4) $\frac{f - a}{2 ( 1 + b )}$ 41. $The trajectory of a projectile projected from origin is given by the equation y = x - \frac{2 x ^{2}}{5} . The initial velocity of the projectile is$ (1) $25 m s^{- 1}$ (2) $\frac{2}{5} m s^{- 1}$ (3) $\frac{5}{2} m s^{- 1}$ (4) $5 m s^{- 1}$ 42. $Two cars A and B initially at rest are moving in same direction with accelerations a_{1} and a_{2}, respectively. After a certain time, they achieve velocities v_{1} and v_{2} and separated by a distance of 50 m . If (a_{1} - a_{2}) = 4 ms^{- 2}, then the quantity (v_{1} - v_{2}) will be$ (1) $24 ms^{- 1}$ (2) $20 ms^{- 1}$ (3) $40 ms^{- 1}$ (4) $12 ms^{- 1}$ 43. $A projectile is thrown upward at an angle 60^{\circ} with the horizontal. The speed of the projectile is 20 m / s when its direction of motion is 45^{\circ} with the horizontal. The initial speed of the projectile is____m / s .$ (1) $202$ (2) $40$ (3) $402$ (4) $203$ 44. $A body travels 102.5 m in n^{th} second and 115.0 m in (n + 2)^{th} second. The acceleration is :$ (1) $6.25 m / s^{2}$ (2) $12.5 m / s^{2}$ (3) $9 m / s^{2}$ (4) $5 m / s^{2}$ 45. $Consider a car initially at rest, starts to move along a straight road first with acceleration 5 m / s^{2}, then with uniform velocity and finally, decelerating at 5 m / s^{2}, before coming to a stop. Total time taken from start to end is t = 25 s . If the average velocity during that time is 72 km / hr, the car moved with uniform velocity for a time of$ (1) $15 s$ (2) $30 s$ (3) $155 s$ (4) $2 s$ 46. $A person travelling in a straight line moves with a constant velocity v_{1} for certain distance x and with a constant velocity v_{2} for next equal distance. The average velocity v is given by the relation$ (1) $\frac{1}{v} = \frac{1}{v _{1}} + \frac{1}{v _{2}}$ (2) $\frac{2}{v} = \frac{1}{v _{1}} + \frac{1}{v _{2}}$ (3) $\frac{v}{2} = \frac{v _{1} + v _{2}}{2}$ (4) $v = v_{1} v_{2}$ 47. $A boy throws a ball into air at 45^{\circ} from the horizontal to land it on a roof of a building of height H . If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is____m. (g = 10 m / s^{2})$ (1) $15$ (2) $20$ (3) $25$ (4) $10$ 48. $A particle aimed at a target, projected with an angle 15^{\circ} with the horizontal is short of the target by 10 m . If projected with an angle of 45^{\circ} is away from the target by 15 m, then the angle of projection to hit the target is$ (1) $\frac{1}{2} sin^{- 1} (\frac{1}{10})$ (2) $\frac{1}{2} sin^{- 1} (\frac{3}{10})$ (3) $\frac{1}{2} sin^{- 1} (\frac{9}{10})$ (4) $\frac{1}{2} sin^{- 1} (\frac{7}{10})$ 49. $A body falls freely for 10 sec . Its average velocity during this journey (take g = 10 m s^{- 2})$ (1) $100 m s^{- 1}$ (2) $10 m s^{- 1}$ (3) $50 m s^{- 1}$ (4) $5 m s^{- 1}$ 50. $A motorboat covers a given distance in 6 hours moving downstream on a river. It covers the same distance in 10 hours moving upstream. The time it takes to cover the same distance in still water is$ (1) $9 hours$ (2) $7.5 hours$ (3) $6.5 hours$ (4) $8 hours$ 51. $If 0.5 i + 0.8 j + c k is a unit vector, then c is$ (1) $0.89$ (2) $0.2$ (3) $0.3$ (4) $0.11$ 52. $A ball projected up passes the same height H at 2 s and 10 s . The value of H is [Use g = 9.8 m / s^{2}]$ (1) $102 m$ (2) $100 m$ (3) $98 m$ (4) $9.8 m$ 53. $A stone thrown with velocity ' u' at angles ' θ' and (90^{\circ} - θ) with the horizontal reaches to maximum heights H_{1} and H_{2} respectively. Its horizontal range is$ (1) $4 H_{1} H_{2}$ (2) $2 H_{1} H_{2}$ (3) $2 H_{1} H_{2}$ (4) $4 \frac{H _{1}}{H _{2}}$ 54. $In a sports competition, a javelin in thrown at an angle 45^{\circ}, which recorded a range of 90 m . The maximum height reached by the javelin is (Neglect air resistance and acceleration due to gravity = 10 ms^{- 2})$ (1) $45 m$ (2) $30 m$ (3) $22.5 m$ (4) $302 m$ 55. $A small block slides down on a smooth inclined plane, starting from rest at time t = 0 . Let s_{n} be the distance travelled by the block in the interval t = n - 1 to t = n . Then, the ratio \frac{s _{n}}{s _{n + 1}} is [NEET 202I]$ (1) $\frac{2 n - 1}{2 n}$ (2) $\frac{2 n - 1}{2 n + 1}$ (3) $\frac{2 n + 1}{2 n - 1}$ (4) $\frac{2 π}{2 π - 1}$ 56. $A body of mass m moving along a straight line covers half the distance with a speed of 2 m s^{- 1} . The remaining half of the distance is covered in two equal time intervals with a speed of 3 m s^{- 1} and 5 m s^{- 1} respectively. The average speed of the particle for the entire journey is$ (1) $\frac{3}{8} m s^{- 1}$ (2) $\frac{8}{3} ms^{- 1}$ (3) $\frac{4}{3} ms^{- 1}$ (4) $\frac{16}{3} m s^{- 1}$ 57. $A bullet is fired from a gun at the speed of 280 m s^{- 1} in the direction 30^{\circ} above the horizontal. The maximum height attained by the bullet is (g = 9.8 m s^{- 2}, sin 30^{\circ} = 0.5) [NEET 2023]$ (1) $2000 m$ (2) $1000 m$ (3) $3000 m$ (4) $2800 m$ 58. $A bus travelling the first one‐third distance at a speed of 10 k m / h, the next one‐third at 20 k m / h and at last one‐third at 60 k m / h . The average speed of the bus is$ (1) $9 k m / h$ (2) $16 k m / h$ (3) $18 k m / h$ (4) $48 k m / h .$ 59. $Two bodies of masses ' m_{1}' and ' m_{2}' are dropped from two different heights h_{1} and h_{2} respectively. The ratio of the times taken by the two masses to touch the ground is (neglect air resistance)$ (1) $\frac{h _{1}}{h _{2}}$ (2) $\frac{m _{1} h _{1}}{m _{2} h _{2}}$ (3) $\frac{m _{1} h _{2}}{m _{2} h _{1}}$ (4) $\frac{h _{1}}{h _{2}}$ 60. $Which of the following is not a vector quantity?$ (1) $Momentum$ (2) $Weight$ (3) $Potential energy$ (4) $Nuclear spin$