MBOSE XI 2019 PYQ

12. The position of an object is given by the equation x = 2 + 2.5t², where the constants 2 and 2.5 indicate the displacement and constant acceleration of an object respectively. Find the average velocity between t = 2 sec and t = 4 sec by using calculus. [2] 15. In a hydrogen atom, an electron revolves around the nucleus in a circular orbit of radius 0.45 Å with a speed of 3.1×10⁶ m s⁻¹. Find its angular momentum. [2] 19. (a) Derive an expression for stopping distance for vehicles. (b) A car moving along a straight highway with speed of 126 km h⁻¹ is brought to rest within a distance of 200 m. What is the retardation (assumed uniform) of the car and how long does it take for the car to stop? [3] 26. A 4 kg mass is attached to a spring of spring constant 400 N m⁻¹. It is made to vibrate on a frictionless rod. The mass is displaced through a distance of 10 cm from the equilibrium position and then released. Calculate (a) the time period of oscillation (b) the maximum speed of vibration (c) the maximum acceleration of the attached mass. [1 + 1 + 1 = 3]