Without air resistance, all bodies falling to earth from the same location fall vertically with the same acceleration.

If the distance of fall is small relative to the radius of the earth, the acceleration remains essentially constant throughout the fall.

This idealized situation, with no air resistance and constant acceleration, is called freefall. The kinematic equations can be used.

Acceleration in freefall is called the acceleration due to gravity, symbolized by g.

Near the earth’s surface: g = 9. 80 m/s2 Near the earth’s surface: g = 9.80 m/s2. g decreases with increasing altitude and varies slightly with latitude.

Ex 13 - A stone is dropped from rest from the top of a tall building Ex 13 - A stone is dropped from rest from the top of a tall building. After 3.00 s of freefall, what is the displacement y of the stone?

Ex 14 - After 3.00 s of freefall, what is the velocity v of the stone in the previous example?

The acceleration due to gravity also affects the motion of upward moving objects, decreasing their velocity.

Ex 15 - A referee tosses a coin with an initial speed of 8. 00 m/s Ex 15 - A referee tosses a coin with an initial speed of 8.00 m/s. Neglecting air resistance, how high does the coin go above its point of release?

Ex 16 - What is the total time the coin is in the air?

The coin in the previous example begins with an upward velocity which decreases to zero, then increases in a downward direction, but the downward acceleration due to gravity is constant.

An object tossed upward takes the same amount of time to rise to its peak as it does to fall back to its starting point. Plus, the speed upward at any height is equal to the speed at the same height as the object is falling downward.

Ex 20 - What is the velocity of the coin in the previous two examples at a height of y = +1.50 m?

Velocity and acceleration can be plotted on a graph as displacement vs Velocity and acceleration can be plotted on a graph as displacement vs. time and as velocity vs. time.

In each case, the slope of the line indicates the velocity (rate of change of displacement) and acceleration (rate of change of velocity).

Ex 19 - A bicyclist maintains a constant velocity on the outgoing leg of a journey, zero velocity while stopped for lunch, and another constant velocity on the way back. Using the time and position intervals indicated in Figure 2.24, obtain the velocities for each segment of the trip.

If an object is accelerating, a position vs If an object is accelerating, a position vs. time graph will be a curved line. The velocity at any instant in time is the slope of a line tangent to the curve at that point.

The slope of the line of a velocity vs The slope of the line of a velocity vs. time graph is the average acceleration.