Chapter 2 Uniformly Accelerated Motion

ACCELERATION is the final velocity is the initial velocity is the time to change velocity Units – m/s2, ft/s2, etc.

For the acceleration tangent to the path of motion

UNIFORMLY ACCELERATED MOTION ALONG A STRAIGHT LINE This is constant acceleration in a straight line. The vector nature can be specified with + and - signs.

These equations are all you need to work most uniform accelerated motion problems.

DIRECTION IS IMPORTANT Choose a positive direction and a negative direction.

GRAPHICAL INTERPRETATIONS A distance versus time curve always has a positive slope. A displacement versus time curve is not that restrictive. The slope on a displacement versus time curve is the instantaneous velocity. The slope on a velocity versus time curve is the instantaneous acceleration.

Consider the function Plotted x(m) t(s) v(m/s) t(s) a(m/s2) t(s) 16 32 16 32 t(s) 2 4 6 v(m/s) 12 -12 -24 -36 2 4 6 t(s) a(m/s2) 12 -12 -24 2 4 6 t(s)

ACCELERATION DUE TO GRAVITY (g) The acceleration due to gravity is down and equals

VELOCITY COMPONENTS Consider projectile motion. q Speed is always positive, however, velocity components have direction.

PROJECTILE PROBLEMS Consider projectile motion with no air resistance. Simply consider two motions: Horizontal motion is constant speed Vertical motion is constant accelerated motion. Useful equations are:

Remember that

Supplementary Problem 2.22 For the object whose motion is plotted in Fig. 2-2, find its instantaneous velocity at the following times: (a) 1.0 s, (b) 4.0 s, and (c) 10 s.

14 12 10 8 Displacement along the y-axis (m) 6 4 2 5 10 15 Time (s)

14 12 10 8 Displacement along the y-axis (m) 6 4 2 5 10 15 Time (s)

14 12 10 8 Displacement along the y-axis (m) 6 4 2 5 10 15 Time (s)