Velocity-Velocity is the derivative of the position-Velocity is a vector. It has direction and magnitude.-Velocity is the antiderivative of the acceleration
Acceleration-Acceleration is the derivative of velocity and the second derivative of position:a(t) = v’(t) = r’’(t)-Acceleration is a vector and has direction and magnitude.
SpeedSpeed is the absolute value of velocity.Object moves along a line: speedObject moves along a curve in a plane: speedSpeed is the magnitude (length) of the velocity vector.Speed is not a vector; it has no direction.Speed is non-negative.
DefinitionsLet the position vector for a point P(x,y) moving in an xy-plane be r(t) =x,y=⟨⟩f(t),g(t), where t is time andf and g are twice differentiable. The velocity, speed,⟨⟩and acceleration of P at time t, respectively, are:
Example 1The position vector of a point P moving in an xy-plane is r(t) =t⟨2+t,t3for 0≤t≤1.⟩Find the velocity and acceleration of P at time t.v(t) = r’(t) = 2t+1,3t