3.1.I.sagews

from sympy import *
from sympy import N as Num

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)

symbolic = True
# symbolic = False

if symbolic:
    # quantity = symbol:
    a0, b, h, alpha, g = var("a0, b, h, alpha, g",  positive=True)
else:
    # factors:
    a0_val = 1
    (b_val, h_val) = (1, 1)
    alpha_val = 1
    g_val = 1
    #
    # quantity =  factor times unit:
    a0 = a0_val*m/s
    (b, h) = (b_val*m, h_val*m)
    alpha = alpha_val
    g = g_val*m/s/s

print("\n--- a: ------------------------------")

t, tb = var("t, t_b", positive=True)

a = 6*a0*t/tb

v = integrate(a,t)
pprint(["v", collect(v,a0)])

S = integrate(v,t)
pprint(["S", collect(S,a0)])

print("\n--- b: ------------------------------")
# sb = s(t=tb)
sb = S.subs(t,tb)
sol = solve(Eq(sb, b), tb)

# new variable tl:
tb = sol[0].simplify()
pprint(["t_b", tb])

# vb = v(t=tb)
print("v")
pprint(v)
vb = v.subs(t,tb).simplify()
print("vb")
pprint(vb)

--- a: ------------------------------ 2 3*a0*t [v, -------] t_b 3 a0*t [S, -----] t_b --- b: ------------------------------ ___ \/ b [t_b, ------] ____ \/ a0 v 2 3*a0*t ------- t_b vb 3*b --- t_b