Arock is thrown vertically upward from the ground, with an initial velocity of 64 ft/sec. its position function is s(t) = –16t2 + 64t. what is its velocity in ft/sec when it hits the ground?

Explanation:

Its position function is s(t) = –16t² + 64t

When it reaches back ground s(t) = 0 ft

Substituting

                s(t) = –16t² + 64t = 0

                          t² - 4t = 0

                           t²  = 4t

                           t =4 seconds

Now we need to find velocity when it reaches ground, that is velocity after 4 seconds.

Differentiating s(t) equation

                   v(t) = -32t+64

            Substituting t = 4 seconds

                  v(4) = -32 x 4+64  = -64 ft/s

Velocity of rock when it hits the ground is -64 ft/s

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

there are no components of a physical goal mentioned on the list of choices that you've provided.