Question

3. 1.25 points SerPSE10 5.C.OP051. 0/7 Submissions Used A force F(7.00i - 3.25t j) N, with t in units of s, is applied to a 2.00 kg object initially at rest. (a) At what time (in s) will the object be moving with a speed of 15.0 m/s? (Round your answer to at least two decimal places.) My N (b) How far (in m) is the object from its initial position when its speed is 15.0 m/s? (c) What is the total displacement (in m) through which the object traveled at this time? (Express your answer in vector form.) Need Help? Read It

Answer 1

Given Mass-m-2 kg Vi = 0 m/s We know, Lv tEo E0 X- component t=0 DE0 tEo u=0

mv7t Y- component 3.25 t dtmdv -3.25_- mv mvy - -3.25 3 Squaring and adding (1) and (2) (Using all SI units) -(-32 3.25 (2)2 (15)249t2

Put t-p 3.257 900 = 49p + (25) p 4p- 900- 3.252 p2 + 49p-900 0 It is a quadratic equation in p, therefore 3.25 -49± (49)2-4 ) (-900) 3.25 On solving, p= 11.38 or-29.94

Since p - t2 and t is positive and real number p = 11.38 s2 t-3.374 s Hence t 3.37 s Distance-d-7 = (y-0) t 15(3.37 s) = 50.61 m Hence d = 50.55 m

(C) Displacement-f-? (Using all SI units) 7t2 3.25t3 2m 7(3.37)2 3.25(3.37)3 7(3.37) 3.25 2(2) 39.75i 31.10j Hence F39.75i 31.10