Question

if the accaleration of an object is given by dv/dt=v/7, find the position function s(t) if v(0)=1 and s(0)= 2

Answer 1

Explanation:

Integrate with respect to 't' the accel function to get the velocity function:

velocity = v/7 t + c1 when t = 0 this =1 so c1 = 1

velocity = v/7 t + 1 integrate again to find position function

s = v/14 t^2 + t + c2 when t = 0 this equals 2 so c2 = 2

s = v/14 t^2 + t + 2

( Let me know if this is incorrect and I will re-evaluate)