Slide 10.2.pptx - Motion Velocity Velocity is the...

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Motion
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.
Speed Speed is the absolute value of velocity. Object moves along a line: speed Object moves along a curve in a plane: speed Speed is the magnitude (length) of the velocity vector. Speed is not a vector; it has no direction. Speed is non-negative.
Definitions Let 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 and f and g are twice differentiable. The velocity, speed, and acceleration of P at time t, respectively, are:
Example 1 The position vector of a point P moving in an xy-plane is r(t) = t 2 +t,t 3 for 0≤t≤1. Find the velocity and acceleration of P at time t. v(t) = r’(t) = 2t+1,3t

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