There is a spade being held above a flat area of soil. The spade is released and falls vertically. It takes 0.29s for the blade to reach the soil.
Calculate the speed.
The spade penetrates 50mm into the soil. Calculate the average acceleration of the spade in the soil.
Because it is being held vertically, when it is released it accelerates due to gravity. The initial velocity is zero because it is not moving. The equation to use is:
Vf = Vi + gt where Vf is the velocity just before it hits the ground, Vi is the initial velocity, g is 9.8 m/s/s, and t is the time in seconds.
Solving you get: Vf = 0 + 9.8 * 0.29 = 2.842 m/s
Once the spade hits the ground it starts slowing down until it comes to a stop. In this case the final velocity is zero, the initial velocity is the just calculated 2.842 m/s, the distance traveled is 50 mm or 0.050 m, and the rate of slowing (the acceleration is unknown).
The appropriate kinematic equation is: Vf^2 = Vi^2 + 2a(Yf - Yi)
where Vf is the final velocity = 0
Vi is the initial velocity = 2.842 m/s
(Yf - Yi) is the distance traveled = 0.050 m
a is the acceleration you are looking for.
Solving you get:
0^2 = 2.842^2 + 2a(0.50)
a = -8.077 m/s/s The minus sign indicating the spade is slowing down.