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 \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32