Question

1. which of the following statements are true about kinetic energy? include all that apply.

a. kinetic energy is the form of mechanical energy which depends upon the position of an object.
b. if an object is at rest, then it does not have any kinetic energy.
c. if an object is on the ground, then it does not have any kinetic energy.
d. the kinetic energy of an object is dependent upon the weight and the speed of an object.
e. kinetic energy is a scalar quantity.
f. an object has a kinetic energy of 40 j. if its mass were twice as much, then its kinetic energy would be 80 j.
g. an object has a kinetic energy of 40 j. if its speed were twice as much, then its kinetic energy would be 80 j.
h. an object can never have a negative kinetic energy.
i. a falling object always gains kinetic energy as it falls.
j. a 1-kg object is accelerated from rest to a speed of 2.0 m/s. this object gains 4.0 joules of kinetic energy.

Explanation:

Step1: Evaluate Statement B

Kinetic energy formula: $KE = \frac{1}{2}mv^2$. Rest means $v=0$, so $KE=0$. Correct.

Step2: Evaluate Statement E

Scalar quantities have magnitude only; KE has no direction. Correct.

Step3: Evaluate Statement F

KE ∝ mass. Original $KE=40J$, double mass → $KE=80J$. Correct.

Step4: Evaluate Statement H

$m$ positive, $v^2$ non-negative → KE ≥0. Correct.

Step5: Evaluate Statement J

Calculate KE: $KE=\frac{1}{2}(1kg)(2m/s)^2=2J≠4J$. Incorrect.

Step6: Evaluate other statements

A: Position relates to potential energy, not KE. Incorrect.
C: Ground position affects potential energy, not KE. Incorrect.
D: KE depends on mass ($m$), not weight ($mg$). Incorrect.
G: KE ∝ $v^2$, double speed → KE=4×40=160J≠80J. Incorrect.
I: Air resistance may reduce speed, so KE not always gained. Incorrect.

Answer:

B. If an object is at rest, then it does not have any kinetic energy, E. Kinetic energy is a scalar quantity, F. An object has a kinetic energy of 40 J. If its mass were twice as much, then its kinetic energy would be 80 J, H. An object can never have a negative kinetic energy