21401839
Description
Mind Map by Eduardo Ramos, updated more than 1 year ago
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Created by Eduardo Ramos
over 5 years ago
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Rectilinear Kinematics: Continuous
12Motion
- Rectilinear Kinematics
- The kinematics of a particle is characterized by specifying, at any given instant, the particle’s
position, velocity, and acceleration.
- The kinematics of a particle is characterized by specifying, at any given instant, the particle’s
position, velocity, and acceleration.
- Position
- The straight-line path of a particle will be defined using a single coordinate axis s, Fig. 12–1a. The
origin O on the path is a fixed point, and from this point the position coordinate s is used to specify
the location of the particle at any given instant. The magnitude of s is the distance from O to the
particle, usually measured in meters (m) or feet (ft), and the sense of direction is defined by the
algebraic sign on s.
- The straight-line path of a particle will be defined using a single coordinate axis s, Fig. 12–1a. The
origin O on the path is a fixed point, and from this point the position coordinate s is used to specify
the location of the particle at any given instant. The magnitude of s is the distance from O to the
particle, usually measured in meters (m) or feet (ft), and the sense of direction is defined by the
algebraic sign on s.
- Displacement
- The displacement of the particle is defined as the change in its position. For example, if the particle
moves from one point to another, Fig. 12–1b, the displacement is s = s - s
- The displacement of the particle is defined as the change in its position. For example, if the particle
moves from one point to another, Fig. 12–1b, the displacement is s = s - s
- Velocity
- If the particle moves through a displacement s during the time interval t, the average velocity of the
particle during this time interval is vavg = s t If we take smaller and smaller values of t, the
magnitude of s becomes smaller and smaller. Consequently, the instantaneous velocity is a vector
defined as v = lim tS0 (s>t), or (S+ ) v = ds dt
- If the particle moves through a displacement s during the time interval t, the average velocity of the
particle during this time interval is vavg = s t If we take smaller and smaller values of t, the
magnitude of s becomes smaller and smaller. Consequently, the instantaneous velocity is a vector
defined as v = lim tS0 (s>t), or (S+ ) v = ds dt
- Acceleration
- Provided the velocity of the particle is known at two points, the average acceleration of the particle
during the time interval t is defined as aavg = v t Here v represents the difference in the velocity
during the time interval t, i.e., v = v - v, Fig. 12–1e. The instantaneous acceleration at time t is a
vector that is found by taking smaller and smaller values of t and corresponding smaller and smaller
values of v, so that a = lim tS0 (v>t), or (S+ ) a = dv dt
- Provided the velocity of the particle is known at two points, the average acceleration of the particle
during the time interval t is defined as aavg = v t Here v represents the difference in the velocity
during the time interval t, i.e., v = v - v, Fig. 12–1e. The instantaneous acceleration at time t is a
vector that is found by taking smaller and smaller values of t and corresponding smaller and smaller
values of v, so that a = lim tS0 (v>t), or (S+ ) a = dv dt
- Constant Acceleration, a = ac .
- Velocity as a Function of Time. Integrate ac = dv>dt, assuming that initially v = v0 when t = 0. L v v0 dv
= L t 0 ac dt
- Position as a Function of Time. Integrate v = ds>dt = v0 + act, assuming that initially s = s0 when t = 0.
L s s0 ds = L t 0 (v0 + act) dt
- Velocity as a Function of Position. Either solve for t in Eq. 12–4 and substitute into Eq. 12–5, or
integrate v dv = ac ds, assuming that initially v = v0 at s = s0 . L v v0 v dv = L s s0 ac ds
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