Question

The table gives coordinates of a particle moving through space along a smooth curve. yz 2.8 9.5 3.8 0 0.5 3.1 7.7 .4 1.0 4.96,2 3.2 5.9 6.8 2.8 1.5 2,0 7,1 7,6 2.7 (a) Find the average velocities over the time intervals [0, 1], [0.5, 1], [1, 21, and [1, 1.5]. (Round your answers to the nearest tenth.) [0, 1] Vave [0.5, 1] Vave 1, 2]: vave 1, 1.5] Vave the particle at t = 1. (Use the time intervals [0.5, 1] and [1, 1.5] to calculate your answer. Round the speed to two decimal places.) (b) Estimate the velocity and speed v(1) X v(1) Enter a number Need Help? Head t Watch It Taik to a Tutor

Answer 1

ANSWERS Giuew: the answefsla) Now YThe nge veloey time interval tur [o,is: over the ave 2-8 9-5 3.8 O S 3.7 3.4 4.9-2.8 2.1 dt 1-04.96.9 3.2 6.2-9.5 -3.3 155.96.8 .8 At I-0 a.o77.6 2.7 3.a-3.8 = -O.6 dt 1-O 2.1i - 3.3j-0.6K Vave fos,Los, Now dr dt 4.9-3-1 3.6 -05 C-a-7.7 dt 3.2-3.4 dt 1-0-5 Vavg=3-6i-3j- 04K for,Ly 7-1-4.9 2-1 dz at F.6-6.2 1.4 2-1 at 9.7-3.3 F0.5 dt a-1 2.ai+1.4j-0SK Vay

ANSWERS 5.9-4.9 dt IS- 6.8-6.2 dz dt 2.8-3.2 O.8 Vavy ait 1.aj-0.8K 3.60-33-0.4K 2it 12j-0.8 k / velatry the particle Naw, he at t-1 Can be Evaluelead as 3.61-33-0.4K+2it12- o.8K VCi) 5.6i-1.8j-1.aK 2 VC) 2.8i-0.9j-0. 6K Ivalno 3.0