Problem 1:

i. A particle is moving in a straight line has an acceleration a = 2/(0.1V+1) (m/s2). It starts from rest at time t= 0 and at time t the velocity is V.m/s and the displacement is D m. Also D=0 at t=0 sec.

ii. Derive a relationship between time t and the velocity V.

iii. Derive a relationship between displacement D and the velocity V.

iv. Draw V Vs t for 0

Problem 2:

A rocket's trajectory shown in Figure Q2, details the rocket's state of motion after 10 seconds from its launching point A (@ time t= 0). Following are the measured parameters of the state of motion after 10 secs:

i. For this instant determine the angle β between the horizontal and the direction of the rocket's trajectory and calculate the velocity and the acceleration of the rocket in i and j directions.

ii. At this instant a rocket detaches it's 1st stage rocket engine module. Calculate the horizontal distance from point A to the 1st stage rocket engine module when it landed on the earth's surface (Assume launching pad and the landing point of 1st stage of rocket are
at the same horizontal plane and neglect the air resistance)

Problem 3:

Figure Q3, shows a small cart of mass M has velocity v m/s enters a smooth circular path (vertical) at A. The cart accelerates along the path and leaves it as a projectile at point B.

I. Determine an expression for angle α.

II. Determine an expression for minimum velocity v that cause cart to leave point A as a projectile.

III. Calculate angle α if the carts initial velocity at v=0 m/s.