Question

What is the acceleration of the particle the first time its velocity equals zero?
s(t)= -4sin(t) - (t/2) +10
What is the acceleration of the particle the first time its velocity equals zero?

−5.197

0.745

1.323

2.550

3.969

Could somebody write out the steps and explain this to me?

Answer 1

have to know how many time derivatives to take.

Answer 2

A particle moves along a line so that at time t, where 0 < t < π, its position is given by

Sorry! this was the first part

Answer 3

s(t)= -4sin(t) - (t/2) +10
v = ds/dt = -4cos t -1/2
a = d^2s/dt^2 = 4 sin t

what is t the first time v = 0?
4 cos t = -1/2
cos t = -1/8
t = 97.2 deg or 360 -97.2
it says the first time so
t = 97.2 deg * pi/180 = 1.7 radians
so what is a?
4 sin 97.2 = 3.97 looks like the last one