12. Intermediate Calculus with Python

Activity 12.01: Finding the Velocity and Location of a Particle

Solution:

1. For the first part, we only have to find where . Let's write functions for dx/dt and dy/dt:

   from math import sqrt,sin,cos,e
   def dx(t):
       return 1 + 3*sin(t**2)
   def dy(t):
       return 15*cos(t**2)*sin(e**t)

2. Now, we can loop from 0 to 1.5 and see where dy/dt goes from positive to negative or vice versa:

   t = 0.0
   while t<=1.5:
       print(t,dy(t))
       t += 0.05

   Here's the important part of the output:

   1.0000000000000002 3.3291911769931715
   1.0500000000000003 1.8966982923409172
   1.1000000000000003 0.7254255490661741
   1.1500000000000004 -0.06119060343046955
   1.2000000000000004 -0.3474047235245454
   1.2500000000000004 -0.04252527324380706
   1.3000000000000005 0.8982461584089145
   1.3500000000000005 2.4516137491656442
   1.4000000000000006 4.5062509856573225
   1.4500000000000006 6.850332845507693...