1. Convert Initial Velocity to m/s:
The initial velocity \( u = 72 \, \text{km/h} \) can be converted to m/s:
\[ u = 72 \times \frac{1000}{3600} = 20 \, \text{m/s}. \]
2. Use Equation of Motion to Find Retardation:
Using \( v = u + at \) with final velocity \( v = 0 \), time \( t = 4 \, \text{s} \):
\[ 0 = 20 + a \times 4. \] Solving for \( a \):
\[ a = -5 \, \text{m/s}^2. \]
3. Calculate Distance Using \( v^2 - u^2 = 2as \):
Substitute values:
\[ 0^2 - 20^2 = 2 \times (-5) \times s. \] Simplifying:
\[ s = 40 \, \text{m}. \]
Answer: 40 m
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: