Free response show reasoning that is complete and correct by the standards of this course. whenever using theorems, you should explicitly check that all hypotheses are satisfied. improper use of (or the absence of) proper notation will be penalized. no cakculator an experimental and theoretical physicist are studying a particle moving along a fixed line (a) taking measurements of the particle's velocity (in it/sec), the experimentalist obtains the sollowing data: t (sec) et) (ft/sec) 0.300 0.230 0100 0.050 0.002 15 30 45 60 approximate the particle's position after 1 minute, prowided the particle's initial position iss (b) using general principles, the theoretical physicist can write the position of the particle as an integral equation compute the velocity of the particle at time t1 minute. does the predicted velocity agree with the experimentally determined velocity? (c) using the integral equation from part (b), compute the position of the paeticle at time1 minute. does the predicted position agree with your approximation from part (a)? (note: tan (2)1107 and tan (4) 1.326)