At any time, t seconds,  a unique particle's location can be pinpointed by using variable coordinates. In the common plane (xy-plane), these are given by

x(t) = 0.5At m
y(t) = Bt² + 5.5 m

where A = 6.3 m/s and B = -0.08 m/s².

After half a minute, what is the magnitude and direction of this particle's acceleration and velocity?

A stone is thrown horizontally from the top of a building with an initial speed of 12 m/s. It takes 4.0 seconds for the stone to hit the ground below. Calculate i) the height of the building, and ii) the horizontal distance from the base of the building to where the stone hits the ground.

A radio-controlled (RC) car with slicks coasts along a smooth tabletop. The motion is two-dimensional and is in the x-y plane and the given graphs show the x and y components of its velocity. Assume that the car's initial position is at the origin. What should be the car's acceleration at t = 10 s?

A motion diagram represents the velocity and acceleration of an object at several different times. In the given motion diagram add the acceleration vectors to complete it.

Commencing with an initial velocity of 12.0 m/s in the westward direction, a boat achieves a velocity of 18.5 m/s northward after a 6.00-second duration. Calculate the magnitude and direction of (i) the average velocity, (ii) the average acceleration throughout this interval, and (iii) the average speed.