is Therefore, the velocity at time tk+2 to calculate the velocity we need to know the velocity at the two previous time steps and . We know = 0 and = = t1 v(t1) v(0) v0. We estimate the velocity at the second time step t2 where we have assumed a constant acceleration in the first time step. We can improve our estimate of by using an average value of the acceleration in the first time step We can now calculate the velocity at all from = to = v(t) t t1 t tN. The acceleration at each time step is The displacement at each time step is EXAMPLE The mscript can be used for simulations for the motion of an mec_fr_mg_bv.m object upon a resistive force of the form (Model 1). Input parameters = 2 kg = 10 kg.s-1 = 10 m.s-1 = 1x10-4 s = 2.00 s m v0 t tmax Outputs N numerical approach A analytical approach terminal velocity = 1.96 m.s-1 vT
Therefore, the velocity at time tk+2 is to calculate the velocity we need to know the velocity at the two previous time steps and . We know t1 = 0 and v(t1) = v(0) = v0. We estimate the velocity at the second time step t2 where we have assumed a constant acceleration in the first time step. We can improve our estimate of by using an average value of the acceleration in the first time step We can now calculate the velocity v(t) at all from t = t1 to t = tN. The acceleration at each time step is The displacement at each time step is EXAMPLE The mscript mec_fr_mg_bv.m can be used for simulations for the motion of an object upon a resistive force of the form (Model 1). Input parameters m = 2 kg = 10 kg.s-1 v0 = 10 m.s-1 t = 1x10-4 s tmax = 2.00 s Outputs N numerical approach A analytical approach terminal velocity vT = 1.96 m.s-1