Lecture 1 Dynamics: 1. Kinematics concerned with the geometric aspects of motion 2. Kinetics - concerned with the forces causing the motion A particle travels along a straight-line path defined by the coordinate axis s. The position of the particle at any
Lecture 2 Given: A particle travels along a straight line to the right with a velocity of v = ( 4 t 3 t2 ) m/s where t is in seconds. Also, s = 0 when t = 0. Find: The position and acceleration of the particle when t = 4 s. Plan: Establish the positive co
Lecture 3 Plots of position vs. time can be used to find velocity vs. time curves. Finding the slope of the line tangent to the motion curve at any point is the velocity at that point (or v = ds/dt). Therefore, the v-t graph can be constructed by finding
Given: The v-t graph shown.
Find: The a-t graph, average speed,
and distance traveled for the 0 - 50 s
Plan: Find slopes of the v-t curve and draw the a-t graph.
Find the area under the curve. It is the distance traveled.
In curvilinear motion, the direction of the instantaneous velocity is always
perpendicular to the hodograph.
tangent to the path.
tangent to the hodograph.
perpendicular to the path.
In curvilinear motion, the direction of the
Acceleration represents the rate of change in the velocity of a particle.
If a particles velocity changes from v to v over a time increment Dt, the average
acceleration during that increment is:
aavg = Dv/Dt = (v - v)/Dt
The instantaneous accele
Given: The box slides down the slope described by the equation y = (0.05x2) m, where x
is in meters.
vx = -3 m/s, ax = -1.5 m/s2 at x = 5 m.
Find: The y components of the velocity and the acceleration of the box at at x = 5 m.
Projectile motion can be treated as two rectilinear motions, one in the horizontal direction
experiencing zero acceleration and the other in the vertical direction experiencing
constant acceleration (i.e., from gravity).
For illustration, consid
Given: A skier leaves the ski jump ramp at qA = 25o and hits the slope at B.
Find: The skiers initial speed vA.
Plan: Establish a fixed x,y coordinate system (in this solution, the origin of the
coordinate system is placed at A). Apply the kinem
The tangential component is tangent to the curve and in the direction of increasing or
at = v
at ds = v dv
The normal or centripetal component is always directed toward the center of curvature of
an = v2/r