If you closed your eyes and were transported to another location, you would not know what your new position is; we do not have a sense of position. If you closed your eyes and were moved at a constant speed, you also would not know. We do not have a sense of velocity, either. However, if your speed changed, or if your direction of motion changed, you would know\u2014we have a sense that detects changes<\/em> in motion. This sense is how we stay balanced and is detected by organs in the inner ear. Large or sudden changes in motion may also be felt in your gut.<\/p>\n\n\n\n Just like velocity is the rate of change of displacement, acceleration<\/em> is the rate of change of velocity:<\/p>\n\n\n \\[ Or, in symbols (for motion along the \\(x\\) axis):<\/p>\n\n\n \\[ The SI unit for acceleration is meters per second per second (m\/s\/s), more commonly expressed as meters per second squared (m\/s2<\/sup>). Since velocity is a vector, acceleration must also be a vector. For two-dimensional motion, we use the rate of change of each component of the velocity:<\/p>\n\n\n \\[ However, the direction of acceleration alone does not tell you anything about which direction you are traveling; it only tells you how the velocity is changing<\/em>. If your acceleration is in the same direction as your velocity (whether that is positive or negative) you are “speeding up;” the magnitude of your velocity is increasing. Conversely, if your acceleration is in the opposite direction as your velocity, you are “slowing down.” (In physics we generally do not use the term “deceleration.”) This is summarized for one-dimensional motion in the table below.<\/p>\n\n\n\n
\n \\text{acceleration} = \\frac{\\text{change in velocity}}{\\text{change in time}}
\n\\]<\/p>\n\n\n\n
\n a_x = \\frac{\\Delta v_x}{\\Delta t} \\tag{4.4}
\n\\]<\/p>\n\n\n\n
\n\\vec{a} = \\underbrace{\\left(\\frac{\\Delta v_x}{\\Delta t}\\right)}_{a_x}\\hat{x} + \\underbrace{\\left(\\frac{\\Delta v_y}{\\Delta t}\\right)}_{a_y}\\hat{y} \\tag{4.5}
\n\\]<\/p>\n\n\n\nDirection of \\(\\vec{v}\\)<\/th> Direction of \\(\\vec{a}\\)<\/th> Speed (\\(v\\)) is…<\/th><\/tr><\/thead> +<\/td> +<\/td> Increasing<\/td><\/tr> +<\/td> –<\/td> Decreasing<\/td><\/tr> –<\/td> +<\/td> Decreasing<\/td><\/tr> –<\/td> –<\/td> Increasing<\/td><\/tr><\/tbody><\/table> practice 4.8<\/h4>\n\n\n\n\n