An automobile of mass '\( m \)' accelerates starting from origin and initially at rest, while the engine supplies constant power \( P \). The position is given as a function of time by:
\( \displaystyle \left(\frac{9P}{8m}\right)^{\frac{1}{2}} t^{\frac{3}{2}} \)
\( \displaystyle \left(\frac{9m}{8P}\right)^{\frac{1}{2}} t^{\frac{3}{2}} \)
\(\displaystyle \left(\frac{8P}{9m}\right)^{\frac{1}{2}} t^{\frac{3}{2}} \)
\(\displaystyle \left(\frac{8P}{9m}\right)^{\frac{1}{2}} t^{\frac{2}{3}} \)
A body of mass \( m \) dropped from a height \( h \) reaches the ground with a speed of \( 0.8\sqrt{g h} \). The value of work done by the air-friction is:
Statement I: A cyclist is moving on an unbanked road with a speed of \( 7 \, \text{km h}^{-1} \) and takes a sharp circular turn along a path of radius of \( 2 \, \text{m} \) without reducing the speed. The static friction coefficient is \( 0.2 \). The cyclist will not slip and pass the curve. \( (g = 9.8 \, \text{m s}^{-2}) \)Statement II: If the road is banked at angle of \( 45^\circ \), cyclist can cross the curve of \( 2 \, \text{m} \) radius with the speed of \( 18.5 \, \text{km h}^{-1} \) without slipping.In the light of the above statements, choose the correct answer from the options given below.
