At t₁ = 8.00 s, a football player in a field has velocity components v_x = -3.0 m/s and v_y = 1.6 m/s. The player's average acceleration has a magnitude 0.6 m/s² at a direction 40° measured from the -x-axis toward the +y axis between t = 8.00 s and t = 15.0 s. Determine the player's x- and y-components of velocity at t₂ = 15.00 s.

The pilot of a trainer plane wants to travel due east. A wind that is classified as "storm" by the weather station blows toward the north at a speed of 100 km/hr (approximately 62.1 mi/h). The airspeed of the plane (its speed in still air) is 300.0 km/h (about 186.4 mi/h). Calculate the speed of the trainer plane over the ground. Draw a vector diagram that will help you in solving the problem.

A small disk slides on a very smooth horizontal surface. The variations of the horizontal and vertical components of the disk's velocity are represented in the figure below. At time t = 0, the disk is at the origin. Calculate the disk's position after 2.0 s.

A small robot navigates a grid on the laboratory floor, initially moving 12.0 cm straight along the x-axis in 2.50 s. It then turns 45.0° to the left and continues straight for another 12.0 cm in 2.00 s. Finally, it turns an additional 55.0° to the left, moving another 12.0 cm in 1.60 s. Calculate its magnitude and direction.

A trekker navigates a meandering path for 5.6 hours to ascend a peak. The journey spans 11.6 km, culminating at a summit 860 m high and positioned 9.0 km due north of the commencement point. Assess the trekker's mean speed and the average velocity vector's magnitude and orientation.