Tiêu đề 3. Motion in a Straight Line.pdf ✅

Motion in a Straight Line 9 3.3 Average Velocity and Average Speed 1. A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is (a) v v 1 2 2 + (b) v v v v 1 2 1 2 + (c) 2 1 2 1 2 v v v v + (d) v v v v 1 2 2 2 1 2 2 2 + (Mains 2011) 2. A car moves from X to Y with a uniform speed vu and returns to X with a uniform speed vd. The average speed for this round trip is (a) v vu d (b) v v v v d u d u + (c) v v u d + 2 (d) 2v v v v d u d u + (2007) 3. 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 (a) 10 m/s, 0 (b) 0, 0 (c) 0, 10 m/s (d) 10 m/s, 10 m/s. (2006) 4. A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed v. The average speed is 48 km/h. The value of v is (a) 56 km/h (b) 60 km/h (c) 50 km/h (d) 48 km/h. (1991) 5. A bus travelling the first one-third distance at a speed of 10 km/h, the next one-third at 20 km/h and at last one-third at 60 km/h. The average speed of the bus is (a) 9 km/h (b) 16 km/h (c) 18 km/h (d) 48 km/h. (1991) 6. A car covers the first half of the distance between two places at 40 km/h and another half at 60 km/h. The average speed of the car is (a) 40 km/h (b) 48 km/h (c) 50 km/h (d) 60 km/h. (1990) 3.4 Instantaneous Velocity and Speed 7. Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xP(t) = (at + bt2 ) and xQ(t) = (f t – t 2 ). At what time do the cars have the same velocity? (a) a f b − 1+ (b) a f b + 2 1 ( − ) (c) a f b + 2 1( + ) (d) f a b − 2 1( + ) (NEET-II 2016) 8. If the velocity of a particle is v = At + Bt2 , where A and B are constants, then the distance travelled by it between 1 s and 2 s is (a) 3 2 7 3 A B + (b) A B 2 3 + (c) 3 2 A B + 4 (d) 3A + 7B (NEET-I 2016) 9. The displacement ‘x’ (in meter) of a particle of mass ‘m’ (in kg) moving in one dimension under the action of a force, is related to time ‘t’ (in sec) by t = + x 3. The displacement of the particle when its velocity is zero, will be (a) 4 m (b) 0 m (zero) (c) 6 m (d) 2 m (Karnataka NEET 2013) 10. A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point (a) D (b) A (c) B (d) C (2008) Motion in a Straight Line 3 CHAPTER EduHulk.COM
10 11. The position x of a particle with respect to time t along x-axis is given by x = 9t 2 – t 3 where x is in metres and t in seconds. What will be the position of this particle when it achieves maximum speed along the +x direction? (a) 54 m (b) 81 m (c) 24 m (d) 32 m. (2007) 12. A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t – t3 . How long would the particle travel before coming to rest? (a) 16 m (b) 24 m (c) 40 m (d) 56 m (2006) 13. The displacement x of a particle varies with time t as x = ae–at + bebt , where a, b, a and b are positive constants. The velocity of the particle will (a) be independent of b (b) drop to zero when a = b (c) go on decreasing with time (d) go on increasing with time. (2005) 14. The displacement-time graph of a moving particle is shown below. The instantaneous velocity of the particle is negative at the point (a) E (b) F (c) C (d) D (1994) 15. Which of the following curve does not represent motion in one dimension ? (a) (b) (c) (d) (1992) 3.5 Acceleration 16. A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = bx–2n, where b and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by (a) –2b2 x–2n + 1 (b) –2nb2 e–4n + 1 (c) –2nb2 x–2n – 1 (d) –2nb2 x–4n – 1 (2015 Cancelled) 17. The motion of a particle along a straight line is described by equation x = 8 + 12t – t 3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is (a) 24 m s–2 (b) zero (c) 6 m s–2 (d) 12 m s–2 (2012) 18. A particle moves a distance x in time t according to equation x = (t + 5)–1. The acceleration of particle is proportional to (a) (velocity)3/2 (b) (distance)2 (c) (distance)–2 (d) (velocity)2/3 (2010) 19. A particle moving along x-axis has acceleration f, at time t, given by f f t T = −      0  1 , where f0 and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle’s velocity (vx) is (a) 1 2 0 2 f T (b) f0T2 (c) 1 2 0 f T (d) f0T (2007) 20. Motion of a particle is given by equation s = (3t 3 + 7t 2 + 14t + 8) m. The value of acceleration of the particle at t = 1 sec is (a) 10 m/s2 (b) 32 m/s2 (c) 23 m/s2 (d) 16 m/s2 . (2000) 21. The position x of a particle varies with time, (t) as x = at2 – bt3 . The acceleration will be zero at time t is equal to (a) a 3b (b) zero (c) 2 3 a b (d) a b (1997) 22. The acceleration of a particle is increasing linearly with time t as bt. The particle starts from origin with an initial velocity v0. The distance travelled by the particle in time t will be (a) v t bt 0 1 2 3 + (b) v t bt 0 1 2 2 + (c) v t bt 0 1 3 6 + (d) v t bt 0 1 3 3 + (1995) 23. A particle moves along a straight line such that its displacement at any time t is given by s = (t 3 – 6t 2 + 3t + 4) metres. The velocity when the acceleration is zero is (a) 3 m/s (b) 42 m/s (c) –9 m/s (d) –15 m/s (1994) 3.6 Kinematic Equations for Uniformly Accelerated Motion 24. A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is (g = 10 m/s2 ) (a) 360 m (b) 340 m (c) 320 m (d) 300 m (NEET 2020) EduHulk.COM
Motion in a Straight Line 11 25. A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is (a) h2 = 3h1 and h3 = 3h2 (b) h1 = h2 = h3 (c) h1 = 2h2 = 3h3 (d) h h h 1 2 3 3 5 = = (NEET 2013) 26. A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 m s–2, the velocity with which it hits the ground is (a) 10.0 m/s (b) 20.0 m/s (c) 40.0 m/s (d) 5.0 m/s (2011) 27. 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/s2 ) (a) 75 m/s (b) 55 m/s(c) 40 m/s (d) 60 m/s (2010) 28. A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then (a) S2 = 3S1 (b) S2 = 4S1 (c) S2 = S1 (d) S2 = 2S1 (2009) 29. A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m s–1 to 20 m s–1 while passing through a distance 135 m in t second. The value of t is (a) 12 (b) 9 (c) 10 (d) 1.8 (2008) 30. The distance travelled by a particle starting from rest and moving with an acceleration 4 3 2 m s− , in the third second is (a) 10 3 m (b) 19 3 m (c) 6 m (d) 4 m (2008) 31. Two bodies A (of mass 1 kg) and B (of mass 3 kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is (a) 4/5 (b) 5/4 (c) 12/5 (d) 5/12 (2006) 32. A ball is thrown vertically upward. It has a speed of 10 m/sec when it has reached one half of its maximum height. How high does the ball rise? (Take g = 10 m/s2 ) (a) 10 m (b) 5 m (c) 15 m (d) 20 m (2005) 33. 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/s2 ) (a) more than 19.6 m/s (b) at least 9.8 m/s (c) any speed less than 19.6 m/s (d) only with speed 19.6 m/s (2003) 34. If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is (a) ut (b) 1 2 2 gt (c) ut − gt 1 2 2 (d) (u + gt)t (2003) 35. 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/s2 ) (a) 8 m (b) 20 m (c) 10 m (d) 16 m. (2001) 36. A car moving with a speed of 40 km/h can be stopped by applying brakes after atleast 2 m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping distance? (a) 4 m (b) 6 m (c) 8 m (d) 2 m (1998) 37. If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s, it covers a distance of (a) 1440 cm (b) 2980 cm (c) 20 m (d) 400 m (1997) 38. 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 (a) 5 m/s (b) 12 m/s (c) 3 m/s (d) 4 m/s. (1996) 39. The water drop falls at regular intervals from a tap 5 m above the ground. The third drop is leaving the tap at instant the first drop touches the ground. How far above the ground is the second drop at that instant? (a) 3.75 m (b) 4.00 m(c) 1.25 m (d) 2.50 m.(1995) 40. A car accelerates from rest at a constant rate a for some time after which it decelerates at a constant rate b and comes to rest. If total time elapsed is t, then maximum velocity acquired by car will be (a) ( ) 2 2 α β αβ − t (b) (α β ) αβ 2 2 + t (c) (α β) αβ + t (d) αβ α β t + (1994) 41. The velocity of train increases uniformly from 20 km/h to 60 km/h in 4 hours. The distance travelled by the train during this period is (a) 160 km (b) 180 km (c) 100 km (d) 120 km (1994) EduHulk.COM
12 42. A body starts from rest, what is the ratio of the distance travelled by the body during the 4th and 3rd second ? (a) 7 5 (b) 5 7 (c) 7 3 (d) 3 7 (1993) 43. A body dropped from top of a tower fall through 40 m during the last two seconds of its fall. The height of tower is (g = 10 m/s2 ) (a) 60 m (b) 45 m (c) 80 m (d) 50 m (1992) 44. What will be the ratio of the distance moved by a freely falling body from rest in 4th and 5th seconds of journey ? (a) 4 : 5 (b) 7 : 9 (c) 16 : 25 (d) 1 : 1. (1989) 45. A car is moving along a straight road with a uniform acceleration. It passes through two points P and Q separated by a distance with velocity 30 km/h and 40 km/h respectively. The velocity of the car midway between P and Q is (a) 33.3 km/h (b) 20 2 km/h (c) 25 2 km/h (d) 35 km/h. (1988) 3.7 Relative Velocity 46. Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be (a) t t t t 1 2 2 1 − (b) t t t t 1 2 2 1 + (c) t1 – t2 (d) t t 1 2 2 + (NEET 2017) 47. A bus is moving with a speed of 10 m s–1 on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus? (a) 40 m s–1 (b) 25 m s–1 (c) 10 m s–1 (d) 20 m s–1 (2009) 48. 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 (a) 12 s (b) 8 s (c) 15 s (d) 10 s (1988) 1. (c) : Let S be the total distance travelled by the particle. Let t1 be the time taken by the particle to cover first half of the distance. Then t S v S v 1 1 1 2 2 = = / Let t2 be the time taken by the particle to cover remaining half of the distance. Then t S v S v 2 2 2 2 2 = = / Average speed, vav Total distance travelled Total time taken = = + = + = + S t t S S v S v v v v v 1 2 1 2 1 2 1 2 2 2 2 2. (d) : Average speed = total distance travelled total time taken = + + = + = + s s t t s s v s v v v v v u d u d 1 2 d u 2 2 . 3. (c) : Distance travelled in one rotation (lap) = 2pr \ Average speed = distance time = 2πr t = × × = 2 3 14 100 − 62 8 10 1 . . m s Net displacement in one lap = 0 Average velocity = net displacement time = = 0 0 t . 4. (b) : Total distance travelled = 200 m 1. (c) 2. (d) 3. (c) 4. (b) 5. (c) 6. (b) 7. (d) 8. (a) 9. (b) 10. (d) 11. (a) 12. (a) 13. (d) 14. (a) 15. (b) 16. (b) 17. (d) 18. (a) 19. (c) 20. (b) 21. (a) 22. (c) 23. (c) 24. (d) 25. (d) 26. (b) 27. (a) 28. (b) 29. (b) 30. (a) 31. (a) 32. (a) 33. (a) 34. (b) 35. (c) 36. (c) 37. (d) 38. (a) 39. (a) 40. (d) 41. (a) 42. (a) 43. (b) 44. (b) 45. (c) 46. (b) 47. (d) 48. (d) ANSWER KEY Hints & Explanations EduHulk.COM