An object moving at a velocity of 32 m/s slows to a stop in 4 seconds. What was its acceleration
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Answer:
The momentum of the particle at the end of the 0.13 s time interval is 7.12 kg m/s
Explanation:
The momentum of the particle is related to force by the following equation:
Δp = F · Δt
Where:
Δp = change in momentum = final momentum - initial momentum
F = constant force.
Δt = time interval.
Let´s calculate the x-component of the momentum after the 0.13 s:
final momentum - 8 kg m/s = -7 N · 0.13 s
final momentum = -7 kg m/s² · 0.13 s + 8 kg m/s
final momentum = 7.09 kg m/s
Now let´s calculate the y-component of the momentum vector after the 0.13 s. Since the particle wasn´t moving in the y-direction, the initial momentum in this direction is zero:
final momentum = 5 kg m/s² · 0.13 s
final momentum = 0.65 kg m/s
Then, the mometum vector will be as follows:
p = (7.09 kg m/s, 0.65 kg m/s)
The magnitude of this vector is calculated as follows:
The momentum of the particle at the end of the 0.13 s time interval is 7.12 kg m/s
Explanation:
First we will convert the given mass from lb to kg as follows.
157 lb =
= 71.215 kg
Now, mass of caffeine required for a person of that mass at the LD50 is as follows.
= 12818.7 mg
Convert the % of (w/w) into % (w/v) as follows.
0.65% (w/w) =
=
=
Therefore, calculate the volume which contains the amount of caffeine as follows.
12818.7 mg = 12.8187 g =
= 1972 ml
Thus, we can conclude that 1972 ml of the drink would be required to reach an LD50 of 180 mg/kg body mass if the person weighed 157 lb.