Motion – Simple Problems – Saitech Informatics

Level – STD 9

Constant Velocity:
A bicycle moves with a constant velocity of 5 m/s. How far will it travel in 6 seconds?
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?
Change in Velocity:
A skateboarder speeds up from 2 m/s to 10 m/s over 4 seconds. How much did their velocity change?
Acceleration:
A sled starts from rest and accelerates uniformly to 12 m/s over 6 seconds. What is its acceleration?
Retardation (Deceleration):
A car traveling at 15 m/s slows down to a stop in 3 seconds. What is its rate of deceleration?
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?
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?
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?
Acceleration:
A toy car starts from rest and reaches a velocity of 8 m/s in 4 seconds. What is its acceleration?
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

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