Kinematics of Particle (KOP) - General Questions

A car is traveling at a speed of 80 ft/s when the brakes are suddenly applied, causing a constant deceleration of 10 ft/s². Determine the time required to stop the car and the distance traveled before stopping.

A small metal particle passes downward through a fluid medium while being subjected to the attraction of a magnetic field such that its position is observed to be s = (15t³ - 3t) mm, where t is measured in seconds. Determine (a) the particle's displacement from t = 2 s to t = 4 s, and (b) the velocity and acceleration of the particle when t = 5 s.

For a short time the missile moves along the parabolic path y = (18 - 2x²) km. If motion along the ground is measured as x = (4t - 3) km, where t is in seconds, determine the magnitudes of the missile's velocity and acceleration when t = 1 s.

The boy throws a snowball such that it strikes the wall of the building at the maximum height of its trajectory. If it takes t = 1.5 s to travel from A to B, determine the velocity v_A at which it was thrown, the angle of release , and the height h.

A fly traveling horizontally at a constant speed enters the open window of a train and leaves through the opposite window 3 m away 0.75 s later. If the fly travels perpendicular to the train's motion as seen from an observer on the ground, and the train is traveling at 3 m/s, determine the speed of the fly as observed by a passenger on the train.

A train travels along a horizontal circular curve that has a radius of 200 m. If the speed of the train is uniformly increased from 30 km/h to 45 km/h in 5 s, determine the magnitude of the acceleration at the instant the speed of the train is 40 km/h.

The block B is suspended from a cable that is attached to the block at E, wraps around three pulleys, and is tied to the back of a truck. If the truck starts from rest when x_D is zero, and moves forward with a constant acceleration of a_D = 2 m/s², determine the speed of the block at the instant x_D = 3 m.

As the instant shown, cars A and B are traveling at speeds of 20 mi/h and 45 mi/h, respectively. If B is acceleration at 1600 mi/h² while A maintains a constant speed, determine the magnitudes of the velocity and acceleration of A with respect to B.