# Effect of time on the acceleration of an object initially at rest?

• howsockgothap
In summary, the answer to the question is yes, time does affect the ability of a force to overcome resisting forces.
howsockgothap
Hello,

I recently bought a Dyson vacuum and have been excitedly vacuuming my floors way more than I need to! I have been doing some thinking as well on the matter (yes, vacuuming) and have a physics problem/question. It has been a long time since I studied physics, so I am not equipped to answer this myself. Basically: vacuuming is supposedly more effective if done slowly, and it is much easier to pick up slightly larger objects when moving the vacuum at a slower speed. My question is, is this because there is some effect of time on the acceleration or new motion of an object?

I know acceleration is dV/t, but what I mean is, if the same force (suction) is applied to a dust particle at rest, does the time over which that force is applied affect the force's ability to overcome resisting forces? Is applying the same force for a longer period of time (vacuuming over a larger object, say a piece of confetti, more slowly) actually more effective/ would T be a factor in over coming the equilibrium of negative (gravity) and positive (the Dysons suction) forces? And if so... How? Or is there some other explanation for vacuuming slowly working better, probably related to the vacuums brush or some such thing I'd know nothing about?

(And yes, I have considered sweeping up slightly larger objects first, that option is not as fun! )

Last edited:
howsockgothap said:
if the same force (suction) is applied to a dust particle at rest, does the time over which that force is applied affect the force's ability to overcome resisting forces?
It makes a greater change to the momentum, so gives the particle more speed, and lifts it higher. If the force is not applied long enough the particle will simply drop back down when the hose moves on past it.

## 1. What is the relationship between time and acceleration for an object initially at rest?

The relationship between time and acceleration for an object initially at rest is directly proportional. This means that as time increases, the acceleration of the object also increases.

## 2. Does the mass of the object affect the acceleration?

Yes, the mass of the object does affect the acceleration. According to Newton's Second Law of Motion, the acceleration of an object is inversely proportional to its mass. This means that as the mass of the object increases, the acceleration decreases.

## 3. Can the acceleration of an object initially at rest ever be negative?

No, the acceleration of an object initially at rest can never be negative. This is because acceleration is a measure of the change in velocity over time, and an object at rest has a velocity of 0. Therefore, there is no change in velocity and the acceleration is 0.

## 4. How does the surface on which the object is placed affect its acceleration?

The surface on which the object is placed can affect its acceleration. If the surface is smooth and frictionless, the object will experience a constant acceleration. However, if there is friction present, the acceleration will be reduced due to the opposing force of friction acting on the object.

## 5. What is the formula for calculating the acceleration of an object initially at rest?

The formula for calculating the acceleration of an object initially at rest is a = (v - u) / t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the time elapsed. If the object is initially at rest, the initial velocity, u, will be 0, making the formula a = v / t.

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