![]() Removing the unit vectors which occur on both sides toilets $F=ma$.Ī deceleration (reduction in magnitude of the velocity) means that the acceleration is in the opposite direction to the velocity and perhaps might be $-2\hat x$. Your Newton’s second law equation is a vector equation $\vec F = m\, \vec a$ which can be written as $F \hat x = m\, a \hat x$ where $F$ and $a$ are components of the force and the acceleration in the $\hat x$ direction (positive x-direction). The important difference from the previous notation for the force $\vec G$ is that now the component $F$ can either be a positive or negative value.Ī force $3\, \hat x$ has a component $3$ in the $\hat x$ direction ie it is a vector of length (magnitude) $3$ in the positive x-direction.Ī force $-5\, \hat x=5(-\hat x)$ has a component $-5$ in the $\hat x$ direction ie it is a vector of length (magnitude) $5$ in the negative x-direction. In this case the force can be written as $\vec F = F \,\hat x$ where $F$ is called the component of the force in the $\hat x$ direction. Now suppose that a force $\vec F$ acts parallel to the x-axis and the unit vector in the direction of $x$ increasing is $\hat x$. In this equation $G$ is always positive because it is the magnitude of the force. ![]() I could write a force $\vec G$ as a vector $\vec G = G\,\hat g$ where $\hat g$ is the unit vector in the direction of the force and $G$ is the magnitude of the force. Hence the constant term when acceleration is integrated with respect to time. In summary, acceleration itself tells us nothing about the velocity at which the object is already traveling at, it only tells us how fast and in which direction its velocity is changing. Be careful when distinguishing "decreasing velocity" with "slowing down" the former talks about velocity, while the latter talks about the speed. An object moving to the left and speeding up will have a very different motion compared to an object moving to the right and slowing down, yet both have would negative acceleration as their velocities are both moving to the left on the number line. Both positive and negative acceleration can cause an object to speed up (in the respective directions). That is the job of the term "speed", which tells us the magnitude of the velocity, how far it is from zero. It does not tell us how close to zero on the number line the velocity is. Negative acceleration, on the other hand, means that the object's velocity is decreasing (either slowing down in the positive direction or speeding up in the negative direction) i.e. When acceleration is positive, it tells us that the velocity is moving to the right on the number line. It may look like a scalar in this case, but it really is a vector. In a one-dimensional problem, its direction is uniquely determined by its sign (there are only 2 possible directions positive and negative). Acceleration is the time derivative of velocity and is a vector. When you choose a direction to be "positive", you're choosing a coordinate system. Positive and negative depends on your chosen coordinate system.
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