*Note: Type-setting limitations do not allow for arrows on the vector labels, so we have used boldface only.Concepts and Skills to Review
Net force: vector addition (Section 2.4)
Free-body diagrams (Section 2.4)
Gravitational force (Section 2.5)
Internal and external forces (Section 2.4)
Summary
Position (symbol r) is a vector from the origin to an object's location. Its magnitude is the distance from the origin and its direction points from the origin to the object.
Displacementis the change in position: Δr = rf - r0 . The displacement depends only on the starting and ending positions, not on the path taken. The magnitude of the displacement vector is not necessarily equal to the total distance traveled; it is the straight line distance from the initial position to the final position.
Vector components: If A points along the +x-axis, then Ax= +A; if A points in the opposite direction-along the negative x-axis-then Ax= -A. When adding or subtracting vectors, we can add or subtract their components.
The average velocity states at what constant speed and in what direction to travel to cause that same displacement in the same amount of time.
Velocity is a vector that states how fast and in what direction something moves. Its direction is the direction of the object's motion and its magnitude is the instantaneous speed.
Average acceleration is the constant acceleration that would give the same velocity change in the same amount of time. In terms of changes in velocity and time,
Acceleration does not necessarily mean speeding up. A velocity can also change by decreasing speed or by changing directions.
Interpreting graphs: On a graph of x(t), the slope at any point is vx . On a graph of vx(t), the slope at any point is ax and the area under the graph during any time interval is the displacement during that time interval. If vx is negative, the displacement is also negative, so we must count the area as negative when it is below the time axis. On a graph of ax(t) , the area under the curve is the change in vx during that time interval.
Newton's Second Law: Fnet = ma (3-8)
The SI unit of force is the newton; 1 N = 1 kg·m/s2. One newton is the magnitude of net force that gives a 1-kg object an acceleration of magnitude 1 m/s2.
Essential relationships for solving any constant acceleration problem:
if ax is constant during the entire time interval from t = 0 until a later time t,
