f(t)=cos(πt/4)
finding velocity i got
-π/4sin(πt/4)
then i had to find velocity after 3 sec which is v'(3)=-π/4sin(π(3)/4) = -π/4sin(π√2/2)
(-π) (π√2)/4 x 2 = -1/8√2 ft/s
i now have to find when the particle is at rest? how would you do this without graphing?
at rest means velocity = 0
right?
right
the answer is 0, 4, and 8 how do i get that from the equation?
To find when the particle is at rest, we need to find the values of t for which the velocity is zero (v'(t) = 0).
In this case, our velocity function is v(t) = -π/4 sin(πt/4).
To solve v'(t) = 0, we can set -π/4 sin(πt/4) = 0.
Since the sine function equals zero at t = 0, π, 2π, 3π, etc., we have the following possibilities for t:
πt/4 = 0, π, 2π, 3π, ...
To solve for t, we can multiply both sides of the equation by 4/π:
t = 0, 4, 8, 12, ...
So, the particle is at rest at t = 0, 4, 8, 12, and so on.