Motion Olympiad (Class 9 Science)

NSO-style olympiad questions on motion, velocity, acceleration, and graphical analysis. Challenging problems requiring deep conceptual understanding and pr

Motion Olympiad (Class 9 Science)

NSO-style olympiad questions on motion, velocity, acceleration, and graphical analysis. Challenging problems requiring deep conceptual understanding and pr

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TL;DR: NSO-style olympiad questions on motion, velocity, acceleration, and graphical analysis. Challenging problems requiring deep conceptual understanding a…

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NSO-style olympiad questions on motion, velocity, acceleration, and graphical analysis. Challenging problems requiring deep conceptual understanding and pr

Motion Olympiad MCQs with Answers & Explanations

Q1. A car accelerates uniformly from rest. In the first second, it covers 2m. How far will it cover in the second second?

  1. 8 m
  2. 2 m
  3. 4 m
  4. 6 m ✓ (correct)

Explanation: For uniform acceleration from rest: s = 0.5*a*t^2. In 1st second (t=1): 2 = 0.5*a*1, so a = 4 m/s^2. Distance in 2nd second = distance in 2s minus distance in 1s = 0.5*4*4 - 0.5*4*1 = 8 - 2 = 6m.

Q2. A ball is thrown vertically upward with initial velocity 30 m/s. Taking g = 10 m/s^2, what is the maximum height reached?

  1. 45 m ✓ (correct)
  2. 60 m
  3. 90 m
  4. 75 m

Explanation: At the highest point v = 0, so h = u²/(2g) = 30²/(2 x 10) = 900/20 = 45 m.

Q3. An object moving in a circle at constant speed has constant velocity. Is this true or false?

  1. True, if the radius is constant
  2. False, velocity changes due to change in direction ✓ (correct)
  3. True, speed and velocity are the same
  4. False, speed increases continuously

Explanation: Velocity is a vector (has direction). In circular motion at constant speed, direction constantly changes, so velocity changes. Speed is scalar and remains constant, but velocity does not.

Q4. The position-time graph of an object is a straight line. What does this indicate?

  1. The object is accelerating
  2. The object is decelerating
  3. The object is moving at constant velocity ✓ (correct)
  4. The object is at rest

Explanation: A straight line on a position-time graph indicates constant slope, which means constant velocity. If the line is horizontal, the object is at rest (zero velocity). If slanted, constant non-zero velocity.

Q5. Two objects A and B start from rest. A travels with uniform acceleration 2 m/s^2 and B with 3 m/s^2 for 5 seconds. Which statement is true?

  1. A travels more distance
  2. Both travel equal distance
  3. Cannot determine from given info
  4. B travels more distance ✓ (correct)

Explanation: Distance A = 0.5*2*25 = 25m. Distance B = 0.5*3*25 = 37.5m. B travels more distance because its acceleration is greater.

Q6. A train moving at 20 m/s applies brakes and comes to rest in 10 seconds. What is its deceleration?

  1. 2 m/s^2 ✓ (correct)
  2. 20 m/s^2
  3. 10 m/s^2
  4. 0.5 m/s^2

Explanation: Using v = u - at: 0 = 20 - a*10, so a = 2 m/s^2.

Q7. In a velocity-time graph, a curved line indicates what?

  1. Constant velocity
  2. Changing acceleration ✓ (correct)
  3. Constant acceleration
  4. No motion

Explanation: A curved v-t graph indicates the acceleration is not constant (changing acceleration). A straight v-t graph indicates constant acceleration. A horizontal line indicates constant velocity.

Q8. A body travels the first half of a distance at 40 km/h and the second half at 60 km/h. What is its average speed for the whole journey?

  1. 45 km/h
  2. 50 km/h
  3. 48 km/h ✓ (correct)
  4. 52 km/h

Explanation: Average speed is total distance over total time, never the average of the two speeds. For equal DISTANCES the harmonic mean applies: 2(40)(60)/(40+60) = 4800/100 = 48 km/h. The tempting 50 km/h would only be right if the two speeds were held for equal TIMES.

Q9. A car covers the first half of its journey TIME at 40 km/h and the second half of the time at 60 km/h. Its average speed is:

  1. 45 km/h
  2. 55 km/h
  3. 48 km/h
  4. 50 km/h ✓ (correct)

Explanation: For equal time intervals the arithmetic mean applies: (40 + 60)/2 = 50 km/h. Compare this with the equal-distance case, which gives 48 km/h — the same two speeds produce different averages depending on whether distance or time is shared equally.

Q10. A stone is dropped from rest. Taking g = 10 m/s², the ratio of the distances it falls in the 1st, 2nd and 3rd seconds is:

  1. 1 : 3 : 5 ✓ (correct)
  2. 1 : 4 : 9
  3. 1 : 1 : 1
  4. 1 : 2 : 3

Explanation: Distance in the nth second is u + (a/2)(2n − 1), which from rest gives 5(2n − 1): 5 m, 15 m and 25 m, a ratio of 1 : 3 : 5. The ratio 1 : 4 : 9 is the TOTAL distance after 1, 2 and 3 seconds — a classic trap.

Q11. Two trains 120 m and 80 m long move towards each other on parallel tracks at 20 m/s and 30 m/s. How long do they take to completely cross each other?

  1. 5 s
  2. 4 s ✓ (correct)
  3. 2 s
  4. 10 s

Explanation: Moving towards each other, the relative speed is 20 + 30 = 50 m/s. To cross completely, the relative displacement needed is the SUM of the lengths, 120 + 80 = 200 m. Time = 200/50 = 4 s.

Q12. A particle returns to its starting point after moving along a circular track of radius r. Its displacement and distance are respectively:

  1. 2πr and 2πr
  2. 2πr and 0
  3. 0 and 2πr ✓ (correct)
  4. 0 and 0

Explanation: Displacement is the shortest straight line from start to finish; returning to the start makes it zero. Distance is the actual path length covered, which is the full circumference 2πr. This is why average velocity for the trip is zero while average speed is not.

Q13. A ball thrown vertically upward returns to the thrower's hand. Which statement is correct about the whole flight?

  1. Velocity and acceleration are both zero at the highest point
  2. Acceleration reverses direction at the highest point
  3. Acceleration is zero at the highest point
  4. Velocity is zero at the highest point but acceleration is g downward throughout ✓ (correct)

Explanation: At the top the ball is momentarily at rest, so velocity is zero — but gravity never switches off, so the acceleration stays g downward for the entire flight, including that instant. Confusing zero velocity with zero acceleration is the single most common error in this topic.

Q14. A car accelerates uniformly from 10 m/s to 30 m/s while covering 200 m. Its acceleration is:

  1. 2 m/s² ✓ (correct)
  2. 0.5 m/s²
  3. 1 m/s²
  4. 4 m/s²

Explanation: Use v² = u² + 2as, the equation that avoids time: 30² = 10² + 2a(200), so 900 = 100 + 400a, giving 400a = 800 and a = 2 m/s². Choosing this equation rather than solving for time first is what makes the problem quick.

Q15. The area under a velocity-time graph between two instants gives:

  1. The acceleration
  2. The displacement ✓ (correct)
  3. The average speed
  4. The distance always, never displacement

Explanation: The area under a v-t graph gives displacement, and area below the time axis counts as negative. Distance would be the sum of the magnitudes of all the areas. The SLOPE of the same graph gives acceleration.

Frequently Asked Questions

Why is velocity more useful than speed in physics?

Velocity is a vector quantity that includes both magnitude (speed) and direction, giving complete information about motion. Speed alone doesn't indicate where an object is heading. Velocity allows us to predict future position and apply Newton's laws correctly. In circular or curved motion, objects can have constant speed but changing velocity due to direction change.

How do we interpret the area under a velocity-time graph?

The area under a v-t graph represents displacement. If the graph is above the time axis (positive velocity), the area is positive displacement. If below (negative velocity or backward motion), it's negative displacement. For non-uniform motion, breaking the area into geometric shapes (rectangles, triangles) gives the displacement during that time interval.

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