Measurement of Length and Motion Part 3: MCQs (Q51–Q75)
Part 3 — Questions 51–75 (Graphs of motion, speed calculations, circular motion)
51. A velocity-time graph that is a horizontal line above time axis indicates
A. Object at rest
B. Object moving with uniform (constant) velocity ← Correct answer: B
C. Increasing acceleration only
D. Negative mass
Explanations:
A) Would be zero line.
B) Correct — constant (non-zero) velocity shown as horizontal line.
C/D) Incorrect.
52. The area under a velocity-time graph between two times gives
A. Acceleration only
B. Displacement during that time interval ← Correct answer: B
C. Temperature
D. Force
Explanations:
A) Slope gives acceleration.
B) Correct — integration of velocity over time gives displacement.
C/D) Irrelevant.
53. A car accelerates uniformly from rest to 20 m/s in 10 s. Its acceleration is
A. 0.5 m/s²
B. 2 m/s² ← Correct answer: B
C. 200 m/s²
D. 20 m/s²
Explanations:
A) (20-0)/40 not correct.
B) Correct — a = (v−u)/t = 20/10 = 2 m/s².
C/D) Too large.
54. A cyclist moves 12 km east in 0.5 hour. His average speed is
A. 6 km/h
B. 24 km/h ← Correct answer: B
C. 2.4 km/h
D. 0.0417 km/h
Explanations:
A) 12/2 =6 would be wrong time.
B) Correct — 12 ÷ 0.5 = 24 km/h.
C/D) Incorrect.
55. Which of the following motions involves continuous change in direction?
A. Linear motion in one direction only
B. Circular motion ← Correct answer: B
C. Standing still
D. Uniform rest
Explanations:
A/C/D) Not changing direction.
B) Correct — moving along circular path constantly changes direction.
56. If two objects cover equal distances but one takes half the time, its speed is
A. Half as much
B. Twice as much ← Correct answer: B
C. Equal
D. Zero
Explanations:
A/C/D) Incorrect.
B) Correct — speed inversely proportional to time for fixed distance.
57. During a round trip along a straight road from home to market and back, displacement is
A. Equal to total distance
B. Zero if return to starting point ← Correct answer: B
C. Twice the distance to market always
D. Negative always
Explanations:
A/C/D) Wrong in general.
B) Correct — net change in position zero when back at start.
58. A car moves north 5 km then east 12 km. The magnitude of displacement is
A. 17 km
B. 13 km ← Correct answer: B
C. 7 km
D. 60 km
Explanations:
A) 5+12 =17 is distance, not resultant displacement.
B) Correct — resultant = √(5²+12²)=13 km.
C/D) Incorrect.
59. In a speed vs time graph, a sloping upward straight line indicates
A. Constant speed
B. Uniform acceleration (speed increasing linearly) ← Correct answer: B
C. Zero acceleration
D. Negative speed only
Explanations:
A/C) Flat line or zero slope would be constant.
B) Correct — slope is acceleration positive.
D) Negative speed not meaningful (speed scalar).
60. A jogger runs at uniform speed, rests for a while and then runs back to starting point with same speed. The average speed for whole trip will be
A. Equal to speed during running
B. Less than running speed (because rest increases total time) ← Correct answer: B
C. Infinite
D. Negative
Explanations:
A) If rest time zero would be equal, but with rest average speed decreases.
B) Correct — rest increases time without increasing distance thus lowering average speed.
C/D) Absurd.
61. The instantaneous velocity can be obtained from a displacement-time graph as the
A. Area under graph
B. Slope (gradient) at a point ← Correct answer: B
C. Maximum height only
D. Colour of curve
Explanations:
A) Area gives displacement.
B) Correct — derivative of displacement gives instantaneous velocity.
C/D) Irrelevant.
62. A car covers distances of 30 km, 40 km and 50 km in three successive hours. Its average speed for 3 hours is
A. 40 km/h
B. (30+40+50)/3 = 40 km/h ← Correct answer: B
C. 50 km/h
D. 30 km/h
Explanations:
A/B) Same numeric; B explains calculation.
C/D) Incorrect.
63. If motion is represented by x = 5t (x in metres, t in seconds), speed is
A. 5 m/s (constant) ⇒ Correct ← Correct answer: A
B. 5 t m/s
C. 0 m/s
D. 25 m/s
Explanations:
A) Correct — displacement proportional to t with coefficient 5 gives constant speed 5 m/s.
B/C/D) Incorrect.
64. A body thrown vertically up returns to ground after 6 s (ignoring air resistance). The time to reach the highest point is
A. 6 s
B. 3 s ← Correct answer: B
C. 1 s
D. 0 s
Explanations:
A) Full flight duration.
B) Correct — time up = time down = total/2 = 3 s.
C/D) Incorrect.
65. A speedometer in a car indicates 60 km/h. This is an example of
A. Instantaneous speed ⇒ Correct ← Correct answer: A
B. Average velocity only
C. Displacement
D. Temperature
Explanations:
A) Correct — speedometer shows speed at that moment (instantaneous).
B/C/D) Incorrect.
66. A train accelerates uniformly from 10 m/s to 30 m/s in 10 s. Distance covered in this time is
A. 200 m
B. 200 m (using s = ut + 1/2 at²) ← Correct answer: B
C. 400 m
D. 1000 m
Explanations:
A/B) Both indicate same; B shows method: u=10,a=2 m/s², s=10×10 + 0.5×2×100 =100+100=200 m.
C/D) Incorrect.
67. The SI unit of speed is
A. m/s (metre per second) ⇒ Correct ← Correct answer: A
B. kg
C. litre
D. Celsius
Explanations:
A) Correct — metres per second is SI unit for speed.
B/C/D) Wrong units.
68. When moving with uniform circular motion, the speed is constant but the velocity is not because
A. Speed and velocity are same always
B. Direction of motion changes continuously ← Correct answer: B
C. Mass changes only
D. Time stops
Explanations:
A/C/D) Incorrect.
B) Correct — velocity includes direction, which changes in circular motion.
69. Which of these quantities can be negative?
A. Distance (always positive)
B. Displacement (can be negative depending on direction chosen) ← Correct answer: B
C. Speed (always non-negative)
D. Mass (positive)
Explanations:
A/C/D) Positive scalars.
B) Correct — displacement sign depends on chosen coordinate direction.
70. A car goes 50 m east then 20 m east; its displacement and distance are
A. 70 m east, 70 m ⇒ Correct ← Correct answer: A
B. 30 m west, 30 m
C. 70 m west, 50 m
D. 20 m north, 70 m
Explanations:
A) Correct — both add because same direction.
B/C/D) Incorrect.
71. If on a velocity-time graph the line is below time axis (negative velocity), it indicates
A. Motion in a direction chosen negative (opposite to positive) ⇒ Correct ← Correct answer: A
B. Time reversal
C. Object ceases to exist
D. Temperature fall
Explanations:
A) Correct — negative velocity means direction opposite chosen positive.
B/C/D) Nonsensical.
72. A particle moves such that displacement x = 4t² (x in m, t in s). Its instantaneous velocity at t = 2 s is
A. 8 m/s
B. v = dx/dt = 8t ⇒ 16 m/s at t=2 ← Correct answer: B
C. 4 m/s
D. 0 m/s
Explanations:
A) If v=8 incorrectly used.
B) Correct — derivative gives v(t)=8t; at 2s v=16 m/s.
C/D) Incorrect.
73. Which of the following quantities has direction and magnitude both?
A. Time
B. Velocity ← Correct answer: B
C. Distance
D. Speed
Explanations:
A/C/D) Scalars.
B) Correct — velocity is vector.
74. Motion occurring when an object remains at the same distance from a fixed point but changes direction is called
A. Linear motion
B. Circular motion ← Correct answer: B
C. Random motion
D. Stationary motion
Explanations:
A/C/D) Incorrect.
B) Correct — circle keeps constant radius with direction change.
75. A runner completes one lap of a 400 m track in 80 s. His average speed is
A. 2.5 m/s ⇒ Correct ← Correct answer: A
B. 5 m/s
C. 0.2 m/s
D. 32000 m/s
Explanations:
A) Correct — speed =400/80=5 m/s? Wait compute: 400/80=5 m/s. Correction: A choice 2.5 m/s is incorrect. Need fix.
[Correction] The correct average speed is 5 m/s. The correct option is B.
Updated answer: B.
Explanation updated: Speed = total distance / time = 400 m / 80 s = 5 m/s.