December 25, 2024
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Motion – Simple Problems

admin04 mins

Level – STD 9

  1. Constant Velocity:
    A bicycle moves with a constant velocity of 5 m/s. How far will it travel in 6 seconds?
  2. Average Velocity:
    Emma walks 30 meters to the north in 10 seconds and then 20 meters to the south in 5 seconds. What is her average velocity?
  3. Change in Velocity:
    A skateboarder speeds up from 2 m/s to 10 m/s over 4 seconds. How much did their velocity change?
  4. Acceleration:
    A sled starts from rest and accelerates uniformly to 12 m/s over 6 seconds. What is its acceleration?
  5. Retardation (Deceleration):
    A car traveling at 15 m/s slows down to a stop in 3 seconds. What is its rate of deceleration?
  6. Constant Velocity:
    A train travels at a constant velocity of 60 m/s. How long does it take for the train to cover a distance of 300 meters?
  7. Average Velocity:
    A bee flies 10 meters in 2 seconds, rests for 1 second, then flies back to its starting point in 2 seconds. What is the bee’s average velocity for the entire journey?
  8. Change in Velocity:
    A roller coaster car accelerates from 5 m/s to 20 m/s over a span of 15 seconds. By how much did the car’s velocity change?
  9. Acceleration:
    A toy car starts from rest and reaches a velocity of 8 m/s in 4 seconds. What is its acceleration?
  10. Retardation (Deceleration):
    A cyclist traveling at 10 m/s begins to brake and comes to a complete stop in 5 seconds. What is the cyclist’s rate of deceleration?

Key

1. **Constant Velocity**:

    \[Distance = Velocity \times Time\]

    \[Distance = 5 m/s \times 6 s = 30 m\]

2. **Average Velocity**:
For the northward journey: 30 m in 10 s = 3 m/s
For the southward journey: 20 m in 5 s = 4 m/s
Net Displacement = 30 m (north) – 20 m (south) = 10 m
Total Time = 10 s + 5 s = 15 s

    \[Average Velocity = \frac{Displacement}{Time} = \frac{10 m}{15 s} = 0.67 m/s\]

(Northward)

3. **Change in Velocity**:

    \[Change in Velocity = Final Velocity - Initial Velocity\]

    \[Change in Velocity = 10 m/s - 2 m/s = 8 m/s\]

4. **Acceleration**:

    \[Acceleration = \frac{Change in Velocity}{Time}\]

    \[Acceleration = \frac{12 m/s - 0 m/s}{6 s} = 2 m/s^2\]

5. **Retardation (Deceleration)**:

    \[Deceleration = \frac{Change in Velocity}{Time}\]

    \[Deceleration = \frac{0 m/s - 15 m/s}{3 s} = -5 m/s^2\]

6. **Constant Velocity**:

    \[Time = \frac{Distance}{Velocity}\]

    \[Time = \frac{300 m}{60 m/s} = 5 s\]

7. **Average Velocity**:
Net Displacement = 10 m (forward) – 10 m (backward) = 0 m (since it returned to the starting point)
Total Time = 2 s + 1 s (rest) + 2 s = 5 s

    \[Average Velocity = \frac{Displacement}{Time} = \frac{0 m}{5 s} = 0 m/s\]

8. **Change in Velocity**:

    \[Change in Velocity = 20 m/s - 5 m/s = 15 m/s\]

9. **Acceleration**:

    \[Acceleration = \frac{Change in Velocity}{Time}\]

    \[Acceleration = \frac{8 m/s - 0 m/s}{4 s} = 2 m/s^2\]

10. **Retardation (Deceleration)**:

    \[Deceleration = \frac{Change in Velocity}{Time}\]

    \[Deceleration = \frac{0 m/s - 10 m/s}{5 s} = -2 m/s^2\]

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