b = 2.40
c = -0.120
#a(t) = 2*b + 6*c*t
v(t) = 2*b*t + 3*c*t^2
x(t) = b*t^2 + c*t^3
#print 'acceleration is the second derivative of position:'
#show(plot(a(t),[t,-1,13.5]))
print 'instantaneous velocity is the derivative of position,'
print 'while avg velocity is position over time it took to get there,'
print 'when they are equal, the avg velocity is at its maximum:'
show(plot([v(t),x(t)/t],[t,-1,13.5]))
print 'position:'
show(plot(x(t),[t,-1,13.5]))
instantaneous velocity is the derivative of position, while avg velocity is position over time it took to get there, when they are equal, the avg velocity is at its maximum: instantaneous velocity is the derivative of position, while avg velocity is position over time it took to get there, when they are equal, the avg velocity is at its maximum: |
position:
var('b,c');
solve(2*b*t + 3*c*t^2,t);
[t == -2/3*b/c, t == 0] [t == -2/3*b/c, t == 0] |
|
|