(AKS 1c) A bowler rolls a bowling ball with a speed of 4 m/s. It took 2s to reach the pins at the end of the lane. What is the final speed if the ball accelerated at rate of - 1.2m/s2 ? 8 m/s O 1.6 m/s 2.8 m/s Om/sz

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

At time t=0, a particle is located at the point (3,6,9). it travels in a straight line to the point (5,2,7), has speed 8 at (3,6,9) and constant acceleration 2i−4j−2k. find an equation for the position vector of the particle.

The slope of a velocity time graph over any interval of time gives the during that interval