# Week 4

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.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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…
1. Finding average velocities from displacement vs. time plots
2. Finding the time of flight and height of a ball thrown upwards.
3. 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).
General College Physics