Motion_and_Curvature9-2&3

Speedmagnitude of velocity speed vt 2 r t

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Unformatted text preview: Speed=magnitude of velocity speed =|| v(t ) ||=|| 2 r (t ) = x(t )i + y (t ) j + z (t )k dr || || dt In mechanics it can be shown that: Velocity: 1st time derivative of the position vector • First we present some examples of motion on a curve • Next we discuss the vector functions of a single variable with some examples we will show how vector • Then with some examples we will show how vector functions help in studying motion of curve v(t ) = r′(t ) = Acceleration: 2nd time derivative of the position vector derivative of the position vector Discussion in this section: a(t ) = r′′(t ) = dr dt d 2r dt dt 2 Example: The position vector of a particle at time t is given by 3 a) Find the velocity, speed and acceleration at t=2 sec. b) Find the velocity in the direction u = i+2j-1k 4 1 1/2/2011 Engineering and Physics Examples Engineering and Physics Examples Curvilinear Motion in the Plane A projectile is launched at an angle θ with an initial velocity v 0 = v0 cos θi + v0 sin θj and initial and an initial height s 0 = s0...
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