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.

A boat is traveling along a circular path having a radius of 20 m. Determine the magnitude of the boat's acceleration if at a given instant the boat's speed is v = 5 m/s and the rate of increase in speed is v = 2 m/s².

A particle is moving along a straight line through a fluid medium such that its speed is measured as v = (2t) m/s, where t is in seconds. If it is released from rest at s = 0, determine its positions and acceleration when t = 3 s.