Question

which examples are all true about acceleration? a car will have less acceleration than a truck an elephant will have less acceleration than a cow an empty bus will have more acceleration than a full bus a soccer ball kicked with 5 newtons of force will have less acceleration than a soccer ball kicked with 8 newtons a football thrown with 10 newtons of force will accelerate more than a football thrown with 15 newtons of force a swimming duck with a mass of 25 grams will have less acceleration than a duck with a mass of 10 grams

Explanation:

To solve this, we use Newton's second law \( F = ma \) (or \( a=\frac{F}{m} \)), where \( a \) is acceleration, \( F \) is force, and \( m \) is mass. Acceleration is directly proportional to force and inversely proportional to mass. Let's analyze each option:

Option 1: A car will have less acceleration than a truck

We don’t know the force applied to each. Without knowing \( F \) for both, we can’t compare \( a \) (since \( a=\frac{F}{m} \), and mass of car < mass of truck, but \( F \) is unknown). So this is not necessarily true.

Option 2: An elephant will have less acceleration than a cow

Elephants have greater mass than cows. If the same force is applied (implicitly, as they move due to internal forces or external forces like gravity/ground reaction, assuming similar force generation), from \( a=\frac{F}{m} \), larger mass (\( m \)) means smaller \( a \). So if force is similar, elephant (larger \( m \)) has less \( a \) than cow (smaller \( m \)). This is likely true.

Option 3: An empty bus will have more acceleration than a full bus

Empty bus has less mass (\( m \)) than full bus. If the same force is applied (e.g., engine force), from \( a=\frac{F}{m} \), smaller \( m \) means larger \( a \). So empty bus (smaller \( m \)) has more \( a \) than full bus (larger \( m \)). This is true.

Option 4: A soccer ball kicked with 5N will have less acceleration than one kicked with 8N

Same mass (soccer ball), so \( a=\frac{F}{m} \). Larger \( F \) (8N > 5N) means larger \( a \). So 5N kick gives less \( a \) than 8N kick. This is true.

Option 5: A football thrown with 10N accelerates more than 15N

Same mass (football), \( a=\frac{F}{m} \). 15N > 10N, so 15N should give more \( a \). This is false.

Option 6: A 25g duck has less acceleration than 10g duck

Same force (implicitly, as they swim with similar effort), \( a=\frac{F}{m} \). Larger mass (25g > 10g) means smaller \( a \). So 25g duck has less \( a \) than 10g duck. This is true.

Now, we check which options are all true:

• Option 2 (elephant < cow), Option 3 (empty bus > full bus), Option 4 (5N < 8N), and Option 6 (25g < 10g) follow \( a \propto \frac{1}{m} \) (with similar force) or \( a \propto F \) (with same mass). Let's confirm:

• Elephant vs. Cow: \( m_{\text{elephant}} > m_{\text{cow}} \), same \( F \) → \( a_{\text{elephant}} < a_{\text{cow}} \) (true).
• Empty vs. Full Bus: \( m_{\text{empty}} < m_{\text{full}} \), same \( F \) (engine) → \( a_{\text{empty}} > a_{\text{full}} \) (true).
• 5N vs. 8N Soccer Ball: Same \( m \), \( F_1=5N < F_2=8N \) → \( a_1 < a_2 \) (true).
• 25g vs. 10g Duck: Same \( F \) (swimming), \( m_1=25g > m_2=10g \) → \( a_1 < a_2 \) (true).

(Note: The first option is invalid due to unknown force, and the fifth is false. So the true examples are the second, third, fourth, and sixth.)

Answer:

• An elephant will have less acceleration than a cow
• An empty bus will have more acceleration than a full bus
• A soccer ball kicked with 5 newtons of force will have less acceleration than a soccer ball kicked with 8 newtons
• A swimming duck with a mass of 25 grams will have less acceleration than a duck with a mass of 10 grams