Question

1095 (1999AB, Calculator). A particle moves along the y-axis with velocity given by v(t) = t sin(t?) for t 0. a) In which direction (up or down) is the particle moving at time t = 1.5? Why? b) Find the acceleration of the particle at time t = 1.5. Is the velocity of the particle increasing at t = 1.5? c) Given that y(t) is the position of the particle at time t and that y(0) = 3, find y(2). d) Find the total distance traveled by the particle from t = 0 and 1 = 2.

Answer 1

vt) at Sin (4) tzo Note for the value of it will go upside for any down Lido 11 Now 5 minli 1.61) V 11.5): 105 1.5.4in (225) 1.16710 V the so in upside diration dv - logít?) + t wilt'<27 - dv=Q = 042 Gos Lt) + sin(t?) d+ =) aceleration : 1.3647 at t=1.5 as accleration is the So speed is increasing at t= 1.5 dy - Vi tlinſta) dt 2) dy vet trin (1²) at :) sdy = Steinit af saya at sin (4 dt +C Yu 16-) 68(42) at tio y=3 » 3 7 caso te o ca C: 3472

lyH) Coult) 2 at t=2 y (2) = 2/2 - 201 (4) 1.8268 Ars total distance Darelled in to to. 172 2 vat Ivo t lint t², at 2 I cus&2) G 2 - 1/2 WS 4 - Coso Coso. = 0.82682 Sou