An object is shot vertically upward from the ground with a velocity of 256 ft/sec. Take the acceleration of gravity be equal to 32 ft/sec2. Express the velocity as a function of time, and find the greatest height by antidifferentiation. v(t)=

Explanation:

The equation of kinematics will be used to find the velocity function.

where g is equal to -32 ft/sec2 and v0 is equal to 256 ft/sec.

Therefore, the velocity function is

The position function is the antiderivative of the velocity function.

The greatest height is where the derivative of the position function is equal to zero. So,

Putting this into the position function gives the greatest height.

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