Question 1: What is the speed of:

A) a car that travels 400m in 20 seconds?

B) an athlete who runs 1500m in 4 minutes?

Question 2: A particle moving with uniform acceleration of 2m/s² has a velocity of 4m/s at a certain time. What is the final velocity?

A) 1 second later?

B) 5 seconds later? 




### Question 1: Speed Calculations

Speed is calculated using the formula:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

#### Part A: Car's Speed
Given:
- Distance traveled = 400 meters
- Time taken = 20 seconds

\[
\text{Speed} = \frac{400 \, \text{m}}{20 \, \text{s}} = 20 \, \text{m/s}
\]

**Answer**: The speed of the car is **20 meters per second (m/s)**.

#### Part B: Athlete's Speed
Given:
- Distance traveled = 1500 meters
- Time taken = 4 minutes = 4 × 60 = 240 seconds

\[
\text{Speed} = \frac{1500 \, \text{m}}{240 \, \text{s}} = 6.25 \, \text{m/s}
\]

**Answer**: The speed of the athlete is **6.25 meters per second (m/s)**.

### Question 2: Final Velocity Calculations

To calculate the final velocity of a particle moving with uniform acceleration, we use the formula:

\[
v_f = v_i + a \cdot t
\]

Where:
- \( v_f \) = final velocity
- \( v_i \) = initial velocity (4 m/s)
- \( a \) = acceleration (2 m/s²)
- \( t \) = time 

#### Part A: Final Velocity 1 Second Later
Given:
- Time \( t = 1 \) second

\[
v_f = 4 \, \text{m/s} + (2 \, \text{m/s}^2 \times 1 \, \text{s}) = 4 \, \text{m/s} + 2 \, \text{m/s} = 6 \, \text{m/s}
\]

**Answer**: The final velocity after 1 second is **6 meters per second (m/s)**.

#### Part B: Final Velocity 5 Seconds Later
Given:
- Time \( t = 5 \) seconds

\[
v_f = 4 \, \text{m/s} + (2 \, \text{m/s}^2 \times 5 \, \text{s}) = 4 \, \text{m/s} + 10 \, \text{m/s} = 14 \, \text{m/s}
\]

**Answer**: The final velocity after 5 seconds is **14 meters per second (m/s)**.

---

Would you like more details or have any questions about these calculations?

### Relative Questions
1. How would the speed change if the car traveled 800m in 40 seconds?
2. What would be the athlete's speed if the race was completed in 5 minutes instead of 4 minutes?
3. How does acceleration affect the final velocity over different time intervals?
4. What is the significance of uniform acceleration in motion?
5. How would you calculate the distance traveled by the particle after 5 seconds?

### Tip:
Always ensure that the units of time and distance are consistent when calculating speed. Convert minutes to seconds if needed.

Explore speed and uniform acceleration calculations with examples involving a car and an athlete. Learn how to calculate speed using distance and time, and find the final velocity of a particle under uniform acceleration. Solutions provided for distances of 400m and 1500m with times of 20 seconds and 4 minutes respectively, along with calculations for final velocities after 1 second and 5 seconds.

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