# Week 4

**Reading:**PSE Chap 3, Vectors

**Topics:**This week, we continue our discussion of week 3 on one-dimensional kinematics and the mean speed theorem. I will introduce the equations of one-dimensional kinematics, and will introduce

*vectors*and

*vector algebra*

**Homework Problems:**Due Tuesday of week 5.

- An object starts from rest at the origin and moves along the x-axis with a constant acceleration of 4 m/s^2. What is its average velocity as it goes from x=2 to x=8 meters? Plot the position, velocity, and acceleration versus time for this object. Solution.
- A car, initially at rest travels 20 meters in 4 seconds along a straight line with constant acceleration. What is its acceleration? Make a plot of the position, velocity and acceleration of this car. Solution.
- How far does a car travel in 6 seconds if its initial velocity is 2 m/s and its acceleration is 2 m/s^2 in the forward direction? Solution.
- A particle's position is given by x(t) = 12 t - 3.0 t^2. What is v(t)? What is a(t)? Make a sketch of its position, velocity and acceleration versus time. Is the particle ever at rest? If so, when? Solution.
- Three strings are attached to a small gold ring. One string pulls eastward with a force of 4 lbs. The second string pulls northward with a force of 7 lbs. The third string pulls southwestward with a force of 5 lbs. (a) First, express the net force as a vector with appropriate components (
*i.e.,*east, north, west, south). (b) Now: what is the magnitude of the net force on the ring? (c) Finally, what is the angle that the net force makes (compared to the eastward direction) . Solution.

**Quiz:**None during week 4. We will have a quiz on Monday of week 5.

**Classroom exercises:**As a reminder, these are some of the problems we worked out in class…

- Finding average velocities from displacement vs. time plots
- Finding the time of flight and height of a ball thrown upwards.
- 1-d kinematic equations: the connection between geometry (area under velocity vs time plots), algebra (kinematic equations relating position, velocity and acceleration), and calculus (integrating acceleration to find velocity and again to find position).