acceleration when velocity is at 0?

Question

The equation of motion of a particle, where s is in meters and t is in seconds, is given by the equation below.
s = 7 t 3 - 9 t
(a) Find the velocity and acceleration as functions of t.
v(t) 21t^2-9
a(t) 42t

acceleration at t 3
126m/s

what is the acceleration when velocity is at 0?
is this zerp as well? or how would I get this?

Answer 1

Take the 1'st derivative to get the velocity and the 2'nd derivative to get the acceleration. After that, it's just plug 'n chug.

And no. When the velocity is zero the acceleration is -not- necesarily zero as well. Solve the velocity equation for the time(s) that the velocity is equal to 0 and plug those times into the equation for acceleration.

Doug

Answer 2

given s(t)= 7t^3 -9t
we can get the velocity function through taking the s(t)derivative once and acceleration function by taking the s(t) derivative twice.

so for velocity v(t) =7*3t^2 - 9 = 21t^2 - 9
acceleration a(t) = 2*21t =42t

when t=3, substitute 3 into a(t) =42*3=126

when velocity is zero , v(t) =0 =21t^2 - 9
solving for t, we get = 0.6547 seconds
so, at t=0.6547, a(t) =0.6547*42=27.49

Answer 3

take the two equations

v(t)=21t^2-9 and
a(t)=42t

set v = 0, so
0=21t^2-9
9/21 = t^2
3/7 = t^2
sqrt(3/7) = t

then substitute in for a?

a = 42 (sqrt(3/7))
a = 27.50

isn't that right?

Answer 4

V(t) = 0 = 21.t^2-9
t = sqrt(9/21)
a(sqrt(9/21)) = 42.sqrt(9/21) = 6.sqrt(21) = 27.49 m/s^2