# What is the need of acceleration? [closed]

As we can usually predict the various forces that a body might be undergoing based on its position and its velocity.Hence what is the need of acceleration?

## closed as unclear what you're asking by niels nielsen, John Rennie, Kyle Kanos, JMac, Jon CusterSep 23 at 13:28

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• vote to close based on no prior research. – niels nielsen Sep 23 at 5:19
• user243076, a body that is moving at constant velocity has no net force acting on it. You seriously need to READ your physics book, and do a little research. – David White Sep 23 at 5:52

The goal is to use the force law to predict the motion of the object by solving the differential equation

$$m\frac{d^2\mathbf{r}}{dt^2}=\mathbf{F}\left(\mathbf{r},\frac{d\mathbf{r}}{dt}\right).$$

You don’t know where the object is going to be until you solve this equation of motion.

The force tells you the acceleration. The acceleration tells you how the velocity changes. The velocity tells you how the position changes.

Newton’s second law, which determines classical dynamics, is

$$\vec{F} = m \frac{d^2 \vec{x}}{d t^2}.$$

As this is a second order differential equation, you’re right in saying that you only need position and its first derivative to determine a system. However, if you’re doing calculations involving classical dynamics, you’ll have to write down $$d^2 \vec{x} / d t^2$$ a lot. So it helps with both understanding and notation to give this its own name — acceleration.

Acceleration is a quantity of interest in a lot of cases, as it’s directly proportional to force. That’s why it’s so commonly used. Interestingly higher derivatives also have names (e.g. jerk and jounce) though these are far less widely used.