Answer:
a) v(2) = 2m/s, v(3) = -2m/s
b) speed at t = 2s is 2m/s
speed at t = 3s is 2m/s
c) 0 m/s
Explanation:
We can take the derivative of x(t) to find the equation of velocity
v(t) = x'(t) = 10 - 4t
(a) v(2) = 10 - 4*2 = 10 - 8 = 2 m/s
v(3) = 10 - 4*3 = 10 - 12 = -2 m/s
(b) The speed would be the same as velocity without the direction
speed at t = 2s is 2m/s
speed at t = 3s is 2m/s
(c) The average velocity between t = 2s and t = 3s is distance it travels over period of time
The final velocity of the tool is 107.4 m/s
Explanation:
We can solve this problem by using the principle of conservation of energy.
In fact, if air resistance is negligible, the total mechanical energy of the tool is conserved during the fall, so we can write:
where
is the kinetic energy of the tool at the top (zero since it is at rest)
is the gravitational potential energy of the tool at the top, where
m is the mass of the tool
g is the acceleration of gravity
h is the heigth of the tool
is the kinetic energy of the tool just before hitting the ground, where
v is the final speed of the tool
is the gravitational potential energy of the tool at the bottom (zero since the height is zero)
Re-arranging the equation,
where we have
And solving for v,
Learn more about kinetic energy and potential energy:
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