Kinematic Relationships Flashcards
Velocity is the rate of change of
Displacement with time
Acceleration is the rate of change of
Velocity with time
Acceleration is the second differential of
Displacement with time
v = u + at
velocity = initial velocity + accelerationn x time
v= ds/dt
velocity is the rate of change of displacement with time
a = dv/dt = d^2s/dt^2
Acceleration is the rate of change of velocity with time and is the second differential of displacement with time
s = ut + 1/2at^2
displacement = initial velocity x time + 1/2 x acceleration x time^2
v^2 = u + 2as
velocity^2 = initial velocity + 2 x acceleration x displacement
the area under a line on a graph can be found by
integration
the gradient of a curve or a straight line on a DISPLACEMENT-TIME graph is the
instantaneous velocity
the gradient of a curve or straight line on a VELOCITY-TIME graph is the
instantaneous acceleration
the gradient of a curve or straight line on a MOTION-TIME graph represents
instantaneous rate of change and this can be found by differentiation
the area under an ACCELERATION-TIME graph between limits is the
change in velocity
the area under a VELOCITY-TIME graph between limits is the
displacement
Derive v = u + at starting with a = dv/dt
integrate with respect to time ds/dt = at + k at t = 0 ds/dt = u so k = 0 at t = t ds/dt = v thus v = u + at
