Chapter 12, Problem 24P

Q4: As a particle accelerates uniformly it passes successive kilometer marks while traveling at velocities of 4 m/s and then 12 m/s. Determine the particles velocity when it passes the next 3 kilometers mark and the time it takes to travel the 4-km distance.

The motion of a particle is defined by the function  x = at3 - bt2 - ct + d  where x is in centimeters and t is in seconds When is the particle at rest if a = 1.3, b = 3.5, c = 8.3, and d = 5.2?

Gas guns are used to investigate the properties of materi- als subjected to high-velocity impacts. A projectile is accelerated through the barrel of the gun by gas at high pressure. Assume that the acceleration of the projectile in m/s² is given by a = c/s, where s is the position of the projectile in the barrel in meters and c is a constant that depends on the initial gas pressure behind the projectile. The projectile starts from rest at s = 1.5 m and acceler- ates until it reaches the end of the barrel at s = 3 m. Determine the value of the constant c necessary for the projectile to leave the barrel with a velocity of 200 m/s.