If an object is 2 kg and a 10 N force is applied to an object. So, the acceleration is 5 m/s^2. Does it mean that if the same amount of force is applied to an object continuously, the object will increase its speed 5 m/s every one second?
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$\begingroup$ As long as the force acts ... It's Newton's first law ... $\endgroup$– Nehal SameeCommented May 10, 2018 at 11:48
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2 Answers
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Yes, you are correct. Acceleration is defined as the rate of change of velocity, i.e. by how much the velocity changes in a certain amount of time.
Mathematically the acceleration is given by the time derivative of velocity:
$$a=\frac{dv}{dt}$$
which for constant acceleration (constant force) as in this case can also be written as:
$$a=\frac{\Delta v}{\Delta t}$$
So an acceleration of $5~m/s^2$ means that the velocity changes by $\Delta v=5~m/s$ every $\Delta t=1~s$, or (which is equivalent) by $\Delta v=10~m/s$ every $\Delta t=2~s$ or ...
answered May 10, 2018 at 11:51
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It is correct as long as the mass of the object is constant
Newton's second law basically says that force is directly proportional to the rate of change of momentum. In symbols, (considering proportionality constant $= 1$)
\begin{equation}F = \frac{dp}{dt}\end{equation} where p is momentum, the product of mass and velocity, or $$p = mv$$
When m is constant, the first equation reduces to $$F = m\frac{dv}{dt}$$ so for a given force, we have a fixed acceleration. But this is not the case if the mass is not constant.
Usually, the mass changes if:
- Mass is entering or leaving the system, such as in a rocket, which expels the gases produced by combustion of fuel.
- According to special relativity, as the kinetic energy of a body increases, so does its mass. For ordinary velocities, this effect is negligible, but as bodies approach the speed of light, their mass increases, and the corresponding acceleration for the same force, decreases.
