Answer:
-3.15 x 10^-6 J
v = 19.86 m/s (rounded to two decimal places)
Step-by-step explanation:
To calculate the kinetic energy gained by the object, we can use the formula:
K = (1/2)mv^2
where "K" is the kinetic energy gained, "m" is the mass of the object, and "v" is its velocity. We are given that the mass of the object is 16 x 10^-9 kg. To find the velocity of the object, we need to use the conservation of energy principle, which states that the change in potential energy of an object is equal to the change in its kinetic energy. Therefore, we can use the formula:
ΔPE = qΔV
where "ΔPE" is the change in potential energy, "q" is the charge of the object, and "ΔV" is the change in potential. We are given that the charge of the object is -630 nC (note that "nC" stands for nano-coulombs, which is 10^-9 coulombs). The change in potential is 5 volts, since the object accelerates from a potential of 0 volts to 5 volts. Therefore:
ΔPE = (-630 x 10^-9 C) x (5 V) = -3.15 x 10^-6 J
The negative sign indicates that the object loses potential energy as it gains kinetic energy. Since the total energy of the object (potential energy plus kinetic energy) remains constant, we can say that the kinetic energy gained by the object is:
K = -ΔPE = 3.15 x 10^-6 J
Therefore, the kinetic energy gained by the object is 3.15 x 10^-6 J.
To find the velocity of the object, we can rearrange the formula for the kinetic energy and substitute in the values we have:
K = (1/2)mv^2
3.15 x 10^-6 J = (1/2) (16 x 10^-9 kg) v^2
Simplifying:
v^2 = (2 x 3.15 x 10^-6 J) / (16 x 10^-9 kg)
v^2 = 394.6 m^2/s^2
Taking the square root:
v = 19.86 m/s (rounded to two decimal places)
Therefore, the velocity of the object is approximately 19.86 m/s.
Explanations for incorrections:
Your calculation for the kinetic energy gained by the object is correct, but you made a mistake in the calculation of the velocity of the object. The correct value of the velocity is approximately 19.86 m/s, not 19.84 m/s. This is because you rounded the value to two decimal places, whereas the actual value is slightly closer to 19.86 m/s.
When working with calculations involving small values, it is important to keep track of the units and their prefixes carefully. In this problem, you correctly converted the charge of the object from nano-coulombs to coulombs, but you did not convert the mass of the object from nano-kilograms to kilograms. This resulted in a calculation error in the final answer for the velocity of the object.