Question

9) Assume that a moving object has constant acceleration a for all t>0 a) Determine a function, v(t), for the velocity of the object. i. For you function, what is v(0)? ii. Is your v(t) the only possible function or are there other possibilities? iii. Describe all possible v(t) b) Determine a function s(t) for the position of the object. What is s(0)? i. ii. Describe all possible s(t) We know that acceleration due to gravity on earth is about 32 ft/s2 (or 9.8 m/s2) c) Completely describe the position function s(t) for a falling object (you should describe if acceleration is positive or negative and why; if the object was dropped or thrown; where the object was when it was dropped or thrown; the units for position).

Answer 1

(a) Let the initial velocity of object at t = 0 is v_0 and the velocity at time t = v (t) then a = v (t) - v_0/t - 0 = v (t) - v_0/t rightdoublearrow v (t) = v_0 + at (i) v (0) = v_0 (ii) No other possibility (iii) v (t) = v_0 + at (b) v (t) = d s(t)/dt = v_0 + at rightdoublearrow integral^s(t)_s_0 d s (t) = integral^t_0 (v_0 + at) dt = s (t) - s_0 = v_0 t + 1/2 at^2 rightdoublearrow s (t) = s_0 + v_) t + 1/2 at^2 rightdoublearrow s (t) = s_) + v_0 t + 1/2 at^2 (c) For dropping rightarrow If the position function s (t) is measured form dropping then rightarrow s (t) = 1/2 times 9.8 t^2 = 4.9 t^2 For throwing with velocity v_o upward and position s (t) is measure from throwing point the s (t) = v_0 t - 4.9 t^2