Chapter 2&3 Kinematics 2. Instantaneous velocity(瞬时速度)p19-22,p52 The velocity at any instant is obtained from the average velocity by shrinking(缩小) the time interval at closer and closer to o △cF The derivative of position vector n M→>0△ t dt with respect to time F() x(t)i+y()j+(1)k r(t+At =v i +v,j+vk=v(t) O
Chapter 2&3 Kinematics x t i y t j z t k dt d dt dr t r v t ( ) ( ) ( ) lim 0 = + + = = → 2. Instantaneous velocity (瞬时速度) p19-22,p52: v i v j v k v(t) x y z = + + = The velocity at any instant is obtained from the average velocity by shrinking（缩小） the time intervalΔt closer and closer to 0. The derivative of position vector with respect to time
Chapter 2&3 Kinematics 3. Average and Instantaneous Speed(速率)P52: Average speed:p、△ s Average speed= total △ t distance/ total time Instantaneous Speed: v=lim As dS At0 At dt 4.The Relation between the Instantaneous Velocity and Instantaneous Speed The magnitude of instantaneous velocity equals to instantaneous speed(瞬时速度的大小等于瞬时 速率)
Chapter 2&3 Kinematics t S v t = → lim 0 t S d d = 3. Average and Instantaneous Speed (速率)P52: 4.The Relation between the Instantaneous Velocity and Instantaneous Speed The magnitude of instantaneous velocity equals to instantaneous speed (瞬时速度的大小等于瞬时 速率). t S v Average Speed: = Instantaneous Speed: Average speed = total distance / total time
Chapter 2&23 Kinematics 讨论 Speed and velocity Speed is simply a positive number, with units. Velocity, on the other hand, is used to signify both the magnitude(numerical value) of how fast an object is moving and the direction in which it is moving. Velocity is therefore a vector
Chapter 2&3 Kinematics 讨论 Speed and Velocity Speed is simply a positive number, with units. Velocity, on the other hand, is used to signify both the magnitude (numerical value) of how fast an object is moving and the direction in which it is moving. Velocity is therefore a vector