Question

Given information: An object is moving with velocity (in feet per second) described by the function v (t) = 4t + 1. We will reason about the object's position function, 8 (t). Question 1 How much does the position change over the time interval (0,4) Answer with a number only (units are feet) 36

Answer 1

O- VI+) ds(+) = 4 + +1 dt s(t)= Integrating worrit El at both sides 4 + + + + c Where ac is Just constant of Integration, s(t) = 2t + t te s(4) - 2x16 + y te slu) 36+c slo) so, $(4) - 10) = 36 os We Need To know The objects Portium At Another Point say 110) 0-3 As we already have, sx) = 2 + + + + Using 110)=4 s TC = 4 s(t)= 2 +² +++4 [s (2) = 14 sol

I-4 . Vlt) - ds dt I-Sint Integrating warto "it" both sides, Alt) = t t cast tc Possible If Britle let, 1(+) = t t cost to Then slo) ot corso)+6 = 7 But as Grifen (110)= 6 so, Third option is carrect. 0-50 Vlt) = ds dt ett tc Integrating both sides worrit it" st) = et - + + As hijen say object Passition Grisen s(+)= et - 2 2 - k Now, 110)- e -o-k e-ork aso=1-K ly, O = k=1