Middle School Science Quiz: Graph Energy And Speed

What this quiz covers

This quiz focuses on Graph Energy And Speed, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Science.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. Because kinetic energy is proportional to $v^2$, so increases in speed cause larger and larger increases in kinetic energy. (correct answer)
2. Because kinetic energy is proportional to $\frac{1}{v}$, so kinetic energy decreases as speed increases.
3. Because kinetic energy is proportional to $v$, so kinetic energy increases by the same amount for each 1 m/s increase in speed.
4. Because mass changes as speed increases, making the relationship unpredictable.

Question 2

1. Because kinetic energy depends on $v^2$, so equal increases in speed cause larger and larger increases in kinetic energy (correct answer)
2. Because kinetic energy depends on $\tfrac{1}{v^2}$, so it decreases faster at higher speeds
3. Because kinetic energy depends only on mass, not speed
4. Because the graph should not pass through the origin when speed is 0

Question 3

1. $\dfrac{\text{KE}}{v}$
2. $\dfrac{\text{KE}}{v^2}$ (correct answer)
3. $\dfrac{v}{\text{KE}}$
4. $\text{KE} \times v$

Question 4

1. 8 J
2. 12 J
3. 16 J (correct answer)
4. 32 J

Question 5

1. Both graphs should be straight lines because KE is directly proportional to speed
2. Both graphs should be curved upward through the origin, and Cart B's curve should be higher (more KE at the same speed) (correct answer)
3. Cart B's graph should curve downward because larger mass reduces kinetic energy
4. Only Cart A's graph should pass through the origin; Cart B's should start above zero

Question 6

1. A straight line that increases at a constant rate and does not need to pass through the origin
2. A curved line through the origin that gets steeper as speed increases (parabola opening upward) (correct answer)
3. A curved line that starts high at $v=0$ and curves downward as speed increases
4. A horizontal line because kinetic energy stays the same when mass is constant

Question 7

1. KE doubles (multiplies by 2)
2. KE increases by 2 J
3. KE quadruples (multiplies by 4) (correct answer)
4. KE is cut in half

Question 8

1. A straight line that increases at a constant rate
2. A curve that rises more and more steeply (parabola) and passes through the origin (correct answer)
3. A curve that decreases as speed increases
4. A horizontal line (kinetic energy stays the same at all speeds)

Question 9

1. It doubles (2×)
2. It triples (3×)
3. It quadruples (4×) (correct answer)
4. It increases by a constant amount each time speed increases

Question 10

1. 3 J
2. 6 J
3. 9 J (correct answer)
4. 12 J

Question 11

1. Both changes in speed increase KE by 3 J
2. Both changes in speed double KE
3. The 1→2 m/s increase adds 3 J, while the 3→4 m/s increase adds 7 J (correct answer)
4. The 3→4 m/s increase adds less KE because the graph flattens at higher speeds

Question 12

1. Kinetic energy is proportional to speed: doubling speed doubles kinetic energy
2. Kinetic energy is proportional to $\tfrac{1}{v}$: doubling speed halves kinetic energy
3. Kinetic energy is proportional to $v^2$: doubling speed makes kinetic energy 4 times larger (correct answer)
4. Kinetic energy stays the same because the mass is constant

Question 13

1. It doubles (from 6 J to 12 J).
2. It triples (from 6 J to 18 J).
3. It quadruples (from 6 J to 24 J). (correct answer)
4. It increases by 6 J (from 6 J to 12 J).

Question 14

1. Graph KE (J) vs speed $v$ (m/s).
2. Graph KE (J) vs $v^2$ (m$^2$/s$^2$). (correct answer)
3. Graph speed $v$ (m/s) vs KE (J).
4. Graph KE (J) vs $\frac{1}{v}$ (s/m).

Question 15

1. Kinetic energy increases by 3 J for each 1 m/s increase in speed.
2. Kinetic energy is proportional to speed ($\text{KE} \propto v$).
3. Kinetic energy is proportional to the square of speed ($\text{KE} \propto v^2$). (correct answer)
4. Kinetic energy decreases as speed increases.

Question 16

1. Both graphs are straight lines, but the 4 kg line is steeper.
2. Both graphs are upward-curving (parabolic) through the origin, and the 4 kg graph is higher at every speed. (correct answer)
3. The 1 kg graph curves upward, but the 4 kg graph curves downward.
4. Both graphs are identical because mass does not affect kinetic energy.

Question 17

1. The graph gets steeper at higher speeds because the increase in KE for the same 1 m/s change becomes larger (correct answer)
2. The graph becomes less steep at higher speeds because KE increases by smaller amounts
3. The graph stays equally steep because KE increases by the same amount each time
4. The graph must be a straight line since KE is measured in joules

Question 18

1. Correct: KE is proportional to $v$, so the graph should be a straight line
2. Incorrect: because of the $v^2$ term, KE increases faster as speed increases, so the KE vs speed graph is curved upward (correct answer)
3. Incorrect: because of the $m^2$ term, KE increases faster as mass increases, so KE vs speed must be flat
4. Correct: KE stays constant when mass is constant, so the graph should be horizontal

Question 19

1. KE increases at a constant rate with speed (linear relationship)
2. KE decreases as speed increases (inverse relationship)
3. KE is proportional to $v^2$ (nonlinear; increases faster at higher speeds) (correct answer)
4. KE is proportional to $\sqrt{v}$

Question 20

1. A straight line through the origin (constant slope).
2. A curve that starts at the origin and bends upward, getting steeper at higher speeds. (correct answer)
3. A curve that starts above the origin (nonzero KE at zero speed).
4. A curve that bends downward (gets less steep as speed increases).