4. 2D Kinematics

A football at rest is kicked by a football kicker. The ball is in contact with the kicker's foot for 0.050s, during which it experiences an acceleration a = 340 m/s². The ball is launched at an angle of 40° above the ground (x-axis). Calculate the horizontal and vertical components of the launch velocity.

A car is moving with speed 16.0 m/s due south at one moment and 25.7 m/s due east 8.00 s later. Over this time interval, determine the magnitude and direction of (a) its average velocity, (b) its average acceleration. (c) What is its average speed? [Hint: Can you determine all these from the information given?]

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by $\vec{v} = \left[ 5.00~\mathrm{m/s} - (0.0180~\mathrm{m/s^3})t^2 \right] \hat{i} + \left[ 2.00~\mathrm{m/s} + (0.550~\mathrm{m/s^2})t \right] \hat{j}$. What are the magnitude and direction of the car's velocity at $t=8.00s$? (b) What are the magnitude and direction of the car's acceleration at $t=8.00s$?

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s.

Complete the motion diagram by adding acceleration vectors.

An object moves along a curved path in the $xy$-plane, and its velocity vectors are shown at four numbered points. At which numbered point or points is the object speeding up?

For an object moving in two dimensions under uniform circular motion, where does the $a\to$ (acceleration) have its greatest magnitude?