DYNAMICS OF RIGID
BODIES
CEDYNA20
ENGR. VINCE GEM Q. SACDALAN
Kinematics of a Particle: Rectilinear
Motion Concept
Constant Acceleration, 𝒂 = 𝒂𝒄
When the acceleration is constant, each of the three kinematic equations 𝒂𝒄 = dv/dt, v = ds/dt,
and 𝒂𝒄 ds = vdv can be integrated to obtain formulas that relate 𝒂𝒄 , v, s, and t.
• Velocity as a Function of Time - Integrate 𝒂𝒄 = dv/dt, assuming that
initially v = 𝒗𝟎 when t = 0.
Kinematics of a Particle: Rectilinear
Motion Concept
• Position as a Function of Time - Integrate v = ds/dt = 𝒗𝟎 + 𝒂𝒄 t,
assuming that initially s = 𝒔𝟎 when t = 0.
Kinematics of a Particle: Rectilinear
Motion Concept
• Velocity as a Function of Position. Either solve for t in Eq. 1 and
substitute into Eq. 2, or integrate vdv = 𝒂𝒄 ds, assuming that initially v
= 𝒗𝟎 at s = 𝒔𝟎 .
Kinematics of a Particle: Rectilinear
Motion Concept
Summary of Three Kinematics Equations (With Constant Acceleration)
SAMPLE PROBLEMS
A stone is thrown vertically upward from a point on a bridge located 40 m above the water.
Knowing that it strikes the water 4 s after release, determine (a) the speed with which the stone
was thrown upward, (b) the speed with which the stone strikes the water.
SAMPLE PROBLEMS
A motorist is traveling at 54 km/h when she observes that a traffic light 240 m ahead of her turns
red. The traffic light is timed to stay red for 24 s. If the motorist wishes to pass the light without
stopping just as it turns green again, determine (a) the required uniform deceleration of the car,
(b) the speed of the car as it passes the light.
SAMPLE PROBLEMS
A sprinter in a 100-m race accelerates uniformly for the first 35 m and then runs with constant
velocity. If the sprinter’s time for the first 35 m is 5.4 s, determine (a) his acceleration, (b) his final
velocity, (c) his time for the race.
SAMPLE PROBLEMS
As relay runner A enters the 20-m-long exchange zone with a speed of 12.9 m/s, he begins to slow
down. He hands the baton to runner B 1.82 s later as they leave the exchange zone with the same
velocity. Determine (a) the uniform acceleration of each of the runners, (b) when runner B should
begin to run.