How do I work out the distance that an object has travelled…?
Assuming constant acceleration, start with dv(t)/dt = a Integrate between initial and final conditions wrt t. ∫ { u(t1) to v(t) } dv(t) = ∫ {t1 to t} a dt v(t) – u(t1) = a(t – t1) But ds(t)/dt = v(t) ds(t)/dt = a(t – t1) + u(t) = at – at1 + u(t1) ∫ { s(0) to s(t) } ds(t) = ∫ {0 to t} ( at – at1 + u(t1) )dt s(t) – s(0) = ½at² – a*t1*t + u*t1*t s(t) = s(0) + ½at² – a*t1*t + u*t1*t where s(0) is your distance *travelled* at time 0, a your acceleration, t1 the known time at the known speed at u(t1) and t is the time at time t.
