If an object is thrown with an initial velocity of 45 m/s, and you want to determine its acceleration at 7 seconds, additional information is required, specifically whether any forces (like gravity or air resistance) are acting on the object.

Here's the reasoning under typical scenarios:

Case 1: If the object is in free fall (e.g., thrown upwards) in Earth's gravity

• The only force acting is gravity, which gives a constant acceleration of $g = 9.8 \, \text{m/s}^2$ downwards (assuming no air resistance).
• In this case, regardless of the initial velocity (45 m/s), the acceleration due to gravity will always be $-9.8 \, \text{m/s}^2$ (negative because gravity acts downwards).

So, the acceleration at 7 seconds would be $-9.8 \, \text{m/s}^2$, as it’s entirely determined by gravity.

Case 2: If no forces are acting on the object (no gravity or other forces)

• If this were an idealized scenario (no forces), the object would travel at a constant velocity.
• Acceleration is defined as the rate of change of velocity. With no forces acting, velocity wouldn't change, meaning the acceleration would be $0 \, \text{m/s}^2$.

Case 3: If other forces are present (air resistance, friction, etc.)

• You would need to know more about the specific forces (like air resistance), and the acceleration could vary depending on those.

Conclusion:

• If the object is subject to gravity (as in most cases), the acceleration will be $-9.8 \, \text{m/s}^2$.
• If no forces act on the object, the acceleration is 0.

Would you like more details on any specific case or have additional questions?

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Follow-up questions:

1. What would be the velocity of the object at 7 seconds, assuming gravity?
2. How would air resistance affect the object's acceleration over time?
3. If thrown upward, how long would it take for the object to reach its maximum height?
4. What is the displacement of the object after 7 seconds under gravity?
5. How can you calculate the velocity at any given time if an object is under constant acceleration?

Tip: The acceleration of an object under Earth's gravity is always $9.8 \, \text{m/s}^2$, regardless of its initial velocity or mass.