Calculus in Physics (2)

Question

A particle moves according to the position function s(t) = e^6t sin(7t).

 

Enclose arguments of functions in parentheses. For example, sin(2t).

 

(a) Find the velocity function.

 v(t)=

 

 __________

 

(b) Find the acceleration function.

 a(t)=

 

 __________

Answer 1

s(t) = e^6t sin(7t); You’ll need to use the chain rule with product rule.

V(t) = (e^(6t)*7*cos(7t)) +(6*e^(6t)*sin(7t)

= 7(e^(6t)cos(7t))+6(e^(6t)sin(7t))

**Notice that the second term in the velocity function is just the position function which was just solved.

A(t) = 7(6*e^(6t)*cos(7t) -(e^(6t)*7*sin(7t)) +6 (7*e^(6t)*cos(7t)+6*e^(6t)*sin(7t))

=84(e^(6t)cos(7t)) -13(e^(6t)sin(7t)