Motion in One Dimension PDF

## Chapter 2: Motion in a Straight Line ### Average Velocity and Average Speed 1. A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is: * (a) 4v/3 * (b) 3v/4 * (c) v * (d) 2v/3 2. A particle covers half of its tot...

## Chapter 2: Motion in a Straight Line ### Average Velocity and Average Speed 1. A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is: * (a) 4v/3 * (b) 3v/4 * (c) v * (d) 2v/3 2. 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) (v₁+v₂)/2 * (b) v₁v₂/(v₁+v₂) * (c) 2v₁v₂ / (v₁+v₂) * (d) √(v₁² +v₂² ) / (v₁+v₂) 3. A car moves from X to Y with a uniform speed vᵤ and returns to X with a uniform speed vᴅ. The average speed for this round trip is: * (a) vᵤvᴅ / (vᵤ+vᴅ) * (b) vᴅvᵤ / (vᴅ+vᵤ) * (c) (vᵤ+vᴅ) / 2 * (d) 2vᴅvᵤ / (vᴅ+vᵤ) 4. 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 5. 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 6. 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. 7. 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 8. The displacement-time graphs of two moving particles make angles of 30° and 45° with the x-axis as shown in the figure. The ratio of their respective velocity is: * (a) √3:1 * (b) 1:1 * (c) 1:2 * (d) 1:√3 9. 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) = (ft - t²). At what time do the cars have the same velocity?: * (a) (a-f)/(1+b) * (b) (a+f)/(2(b-1)) * (c) (a+f)/(2(1+b)) * (d) (f-a)/(2(1+b)) 10. 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) A + B/3 * (b) A + B/3 * (c) A + 4B / 2 * (d) 3A + 7B / 3 11. 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 12. 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 13. The position x of a particle with respect to time t along x-axis is given by x = 9t², 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 14. 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 15. The displacement x of a particle varies with time t as x = ae⁻αt + be⁻βt, where a, b, α and β are positive constants. The velocity of the particle will: * (a) be independent of B * (b) drop to zero when α = β * (c) go on decreasing with time * (d) go on increasing with time 16. 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 17. Which of the following curve does not represent motion in one dimension? 18. The velocity (v) - time (t) plot of the motion of a body is shown below. The acceleration (a) - time (t) graph that best suits this motion is: 19. 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) -2B²x⁻²ⁿ⁺¹ * (b) -2nB²e⁻⁴ⁿ⁺¹ * (c) -2nB²x⁻²ⁿ⁻¹ * (d) -2nB²x⁻⁴ⁿ⁻¹ 20. The motion of a particle along a straight line is described by equation x = 8 + 12t - t³ 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 21. 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 22. A particle moving along x-axis has acceleration f, at time t, given by f = f₀(1-t/T), 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 (v₁) is: * (a) f₀T² * (b) f₀T²/2 * (c) f₀T * (d) f₀T/2 23. Motion of a particle is given by equation s = (3t³ + 7t² + 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. 24. 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) 2a/3b * (b) zero * (c) a/3b * (d) ab 25. The acceleration of a particle is increasing linearity 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) v₀t + bt²/2 * (b) v₀t + bt²/3 * (c) v₀t + bt³/6 * (d) v₀t + bt³/3 26. A particle moves along a straight line such that its displacement at any time t is given by s = (-6t² + 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 ### Kinematic Equations for Uniformly Accelerated Motion 27. A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m s⁻¹. The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g = 10 m s⁻²): * (a) 64 m * (b) 68 m * (c) 56 m * (d) 60 m 28. The ratio of the distance travelled by a freely falling body in the 1st, 2nd, 3rd and 4th second: * (a) 1:2:3:4 * (b) 1:4:9:16 * (c) 1:3:5:7 * (d) 1:1:1:1 29. 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 30. 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) h₁/3 = h₂/5 = h₃/7 31. 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. 32. 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 33. 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 34. 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 12 s. The value of t is: * (a) 12 * (b) 9 * (c) 10 * (d) 1.8 35. The distance travelled by a particle starting from rest and moving with an acceleration 10/3 m s², in the third second is: * (a) 10/3 m * (b) 19/3 m * (c) 6 m * (d) 4 m 36. 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 37. 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 38. 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 39. 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 gt² * (c) ut - 1/2 gt² * (d) (u + gt)t 40. 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. 41. 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 42. 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 43. 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. 44. 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. 45. A car accelerates from rest at a constant rate a for some time after which it decelerates at a constant rate β and comes to rest. If total time elapsed is t, then maximum velocity acquired by car will be: * (a) (α²- β²)t / αβ * (b) (α²+β²)t / αβ * (c) (α+β)t / αβ * (d) αβt / (α+β) 46. 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) 4:5 * (b) 7:9 * (c) 16:25 * (d) 1:1 47. 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 48. 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 49. What will be the ratio of the distance moved by a freely falling body from rest in 4th and 5th seconds of journey? * (a) 1/3 * (b) 3/5 * (c) 5/7 * (d) 7/9 50. 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 ### Relative Velocity 51. 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) t₁t₂/(t₂-t₁) * (b) t₁t₂/(t₂+t₁) * (c) (t₁-t₂)/2 * (d) (t₁+t₂)/2 52. 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 53. 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 ## Answer Key 1. | | Answer | 2. | 1 | (a) | 3. | 2 | (c) | 4. | 3 | (d) | 5. | 4 | (c) | 6. | 5 | (b) | 7. | 6 | (c) | 8. | 7 | (b) | 9. | 8 | (d) | 10. | 9 | (d) | 11. | 10 | (a) | 12. | 11 | (b) | 13. | 12 | (d) | 14. | 13 | (a) | 15. | 14 | (a) | 16. | 15 | (d) | 17. | 16 | (a) | 18. | 17 | (b) | 19. | 18 | (c) | 20. | 19 | (d) | 21. | 20 | (d) | 22. | 21 | (a) | 23. | 22 | (c) | 24. | 23 | (b) | 25. | 24 | (a) | 26. | 25 | (c) | 27. | 26 | (c) | 28. | 27 | (a) | 29. | 28 | (c) | 30. | 29 | (d) | 31. | 30 | (d) | 32. | 31 | (b) | 33. | 32 | (a) | 34. | 33 | (b) | 35. | 34 | (b) | 36. | 35 | (a) | 37. | 36 | (a) | 38. | 37 | (a) | 39. | 38 | (a) | 40. | 39 | (b) | 41. | 40 | (c) | 42. | 41 | (c) | 43. | 42 | (d) | 44. | 43 | (a) | 45. | 44 | (a) | 46. | 45 | (d) | 47. | 46 | (a) | 48. | 47 | (a) | 49. | 48 | (b) | 50. | 49 | (b) | 51. | 50 | (c) | 52. | 51 | (b) | 53. | 52 | (d) | 54. | 53 | (d) | ## Hints & Explanations 1. (a): Average speed = Total distance / Total time taken * Average speed =s/(t₁+t₂) 2. (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 t₁ = s/2v₁. Let t₂ be the time taken by the particle to cover remaining half of the distance. Then t₂ = s/2v₂.