A car travels a distance 100 m with a constant acceleration and average velocity of 20 m `s^(-1)` . The final velocity acquired by the car is 25 m `s^(-1)`. Find : (i) the initial velocity and (ii) acceleration of car.

Explanation

To solve the problem step by step, we will use the given information about the car's motion:

1. **Given Data:**
- Distance (s) = 100 m
- Average velocity (v_avg) = 20 m/s
- Final velocity (v_f) = 25 m/s

2. **Finding Total Time (t):**
The formula for average velocity is:
\[ v_{avg} = \frac{s}{t} \]
Rearranging this formula to find time (t):
\[ t = \frac{s}{v_{avg}} = \frac{100 \text{ m}}{20 \text{ m/s}} = 5 \text{ s} \]

3. **Finding Initial Velocity (u):**
The formula for average velocity in terms of initial and final velocity is:
\[ v_{avg} = \frac{u + v_f}{2} \]
Rearranging to find initial velocity (u):
\[ 20 = \frac{u + 25}{2} \]
Multiplying both sides by 2:
\[ 40 = u + 25 \]
Solving for u:
\[ u = 40 - 25 = 15 \text{ m/s} \]

4. **Finding Acceleration (a):**
The formula for acceleration is:
\[ a = \frac{v_f - u}{t} \]
Substituting the known values:
\[ a = \frac{25 \text{ m/s} - 15 \text{ m/s}}{5 \text{ s}} = \frac{10 \text{ m/s}}{5 \text{ s}} = 2 \text{ m/s}^2 \]

5. **Final Answers:**
- Initial velocity (u) = 15 m/s
- Acceleration (a) = 2 m/s²