Question

Which of these statement(s) is (are) true? 1\. An object can have zero acceleration and be at rest. 2\. An object can have nonzero acceleration and be at rest. 3\. An object can have zero acceleration and be in motion. a) 1 only b) 1 and 3 c) 1 and 2 d) \(1,2,\) and 3

Short answer

a) Statement 1: An object can have zero acceleration and be at rest. b) Statement 2: An object can have nonzero acceleration and be at rest. c) Statement 3: An object can have zero acceleration and be in motion. d) Statements 1, 2, and 3 are all true. Answer: d) Statements 1, 2, and 3 are all true.

Step-by-step solution

Statement 1: An object can have zero acceleration and be at rest.

This statement is correct. When an object is at rest and not subjected to any additional external force, it maintains its zero acceleration and zero velocity according to Newton's first law of motion.

Statement 2: An object can have nonzero acceleration and be at rest.

This statement is also correct. An object can be momentarily at rest (like when you throw a ball, for example, the highest point where the ball is momentarily at rest) and still have nonzero acceleration (since it is under the influence of gravity).

Statement 3: An object can have zero acceleration and be in motion.

This statement is accurate as well. An object will move at a constant velocity when no external force is acting upon it, resulting in zero acceleration. This is in accordance with Newton's first law of motion, the law of inertia. Since all three statements are true, the correct answer is:

Answer

d) Statements 1, 2, and 3 are all true.

Key concepts

Zero Acceleration

Grasping the concept of zero acceleration is essential for understanding motion. To put it simply, when we say an object has zero acceleration, it's either standing completely still or moving at a constant speed in a straight line. Imagine you're on a train gliding smoothly on tracks without speeding up or slowing down - that's zero acceleration in action.

In physics, acceleration refers to the rate at which the velocity of an object changes. So, if there's zero acceleration, there are no changes in its speed or direction. Objects at zero acceleration maintain their state of motion unless an external force is applied. This ties directly into Newton's first law of motion often referred to as the 'law of inertia', which we'll explore in more depth later on.

Object at Rest

An object at rest is one that isn't moving - like a book lying on a desk or a parked car. According to Newton's first law, an object will remain at rest until a force acts upon it.

This state of rest implies that both the object's velocity and acceleration are zero. But it's worth noting that an object at rest might not be free from forces; it could simply be experiencing balanced forces that result in no movement. The trick in distinguishing whether an object is truly at rest is all about the balance of forces and the resulting motion, or in this case, the lack of motion.

Nonzero Acceleration

Now, nonzero acceleration is when things get moving – quite literally. This is when an object is speeding up, slowing down, or changing direction. It's the thrill you feel when a roller coaster takes off or when a car comes to a sudden stop.

Nonzero acceleration indicates a change in the velocity of an object. This could be due to various forces acting on the object, like gravity, friction, or a push or pull. For instance, when a fruit falls from a tree, it accelerates due to gravity, and this acceleration continues until it hits the ground or is stopped by another force.

Object in Motion

An object in motion continues to cruise along as long as nothing interferes to change its speed or direction. It’s thrilling to watch a hockey puck slide across the ice or a skateboard coast down a ramp; these are perfect examples of objects in motion maintaining their velocity, thanks to the absence of forces significant enough to alter that motion - remember, it's all about that constant velocity if the acceleration is zero.

For an object to change its state of motion – that is, to accelerate or decelerate - an unbalanced force must be applied. Hence, an object in motion with zero acceleration must have balanced or no forces acting on it.

Law of Inertia

The law of inertia, or Newton's first law of motion, tells us that an object will stay at rest or in uniform motion unless acted on by an external force. It's why seatbelts are a must in cars, because if the car stops suddenly, our bodies want to keep moving at the same speed and direction – thanks to inertia.

This law is a fundamental principle in physics that explains the reluctance of an object to change its state of motion. It's why you have to apply force to push a heavy piece of furniture, and then again when you want it to stop moving. The greater the mass of an object, the more inertia it has, and thus, the more force needed to change its motion or bring it to rest.