Motion VectorsDisplacement VectorTime is a ScalarVelocity VectorTangentDerivative of a VectorVelocity GraphAcceleration VectorVector EquationsMotion VectorsMotion VectorsDisplacement VectorDisplacement VectorThe position vector is often The position vector is often designated by .designated by .A change in position is a A change in position is a displacement.displacement.The displacement vector is a The displacement vector is a change in the position change in the position vector.vector.yx2r1r12rrrrTime is a ScalarTime is a ScalarPosition and displacement Position and displacement are vectors.are vectors.Time has a value but no Time has a value but no direction – it’s a scalar.direction – it’s a scalar.Vector quantities can be Vector quantities can be multiplied or divided by time multiplied or divided by time using scalar multiplication.using scalar multiplication.yx2t1t12ttt Velocity VectorVelocity VectorDisplacement divided by Displacement divided by time gives the average time gives the average velocity.velocity.The displacement vector The displacement vector divided by time gives the divided by time gives the average velocity vector.average velocity vector.A person walks from 2.0 km A person walks from 2.0 km north of the gym to 3.0 km west north of the gym to 3.0 km west of the gym in 1.5 h. What is the of the gym in 1.5 h. What is the magnitude of average velocity?magnitude of average velocity?•The magnitude of The magnitude of displacement isdisplacement is•The average velocity is the The average velocity is the magnitude of displacement magnitude of displacement divided by the time.divided by the time.trvavkm 3.622yxdddkm/h 2.4/ tdvavTangentTangentThe average velocity The average velocity becomes the instantaneous becomes the instantaneous velocity for short time velocity for short time intervals.intervals.The same is true for vectors.The same is true for vectors.The instantaneous velocity The instantaneous velocity vector direction is tangent to vector direction is tangent to the curve.the curve.dtrdvyx2r1rvDerivative of a VectorDerivative of a VectorThe derivative of a vector can be computed as a The derivative of a vector can be computed as a derivative of the separate components.derivative of the separate components.jdtdyidtdxdtrdvˆˆdtdyvdtdxvyxVelocity GraphVelocity GraphPosition graph with velocity Position graph with velocity vectorsvectorsVelocity graphVelocity graphyx2r1r1vvyvx2v1v2vAcceleration VectorAcceleration VectorAverage acceleration is the Average acceleration is the ratio of the change in ratio of the change in velocity to the time.velocity to the time.Instantaneous acceleration Instantaneous acceleration is the derivative of the is the derivative of the velocity with respect to time.velocity with respect to time.Both these definitions extend Both these definitions extend to vectors.to vectors.tvvtvaav1222dtrddtvdaVector EquationsVector EquationsLike velocity, acceleration equations can be written by Like velocity, acceleration equations can be written by
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