Question

constant acceleration the velocity of an object moving in a straight - line changes at a constant rate when the object experiences constant acceleration. constant acceleration is a steady change in velocity. that is, the veloc - ity of the object changes by the same amount each second. an example of constant acceler - ation is illustrated by the jet airplane shown in figure 15. the airplanes acceleration may be constant during a portion of its takeoff. readingpoint what is constant acceleration? calculating acceleration acceleration is the rate at which velocity changes. you calculate acceleration for straight - line motion by dividing the change in veloc - ity by the total time. if a is the acceleration, vi is the initial velocity, vf is the final velocity, and t is total time, this equation can be written as follows: acceleration = \\(\frac{change\\ in\\ velocity}{total\\ time}=\frac{(v_f - v_i)}{t}\\) notice in this formula that velocity is in the numerator and time is in the denominator. if the velocity increases, the numerator is pos - itive and thus the acceleration is also positive. for example, if you are coasting downhill on a bicycle, your velocity increases and your accel - eration is positive. if the velocity decreases, then the numerator is negative and the acceleration is also negative. for example, if you con - tinue coasting after you reach the bottom of the hill, your velocity decreases and your acceleration is negative. remember that acceleration and velocity are both vector quanti - ties. thus, if an object moving at constant speed changes its direction of travel, there is still acceleration. in other words, the acceleration can change even if the velocity is constant. think about a car moving at a constant speed as it rounds a curve. because its direction is changing, the car is accelerating. to determine a change in velocity, subtract one velocity vector from another. if the motion is in a straight line, however, the velocity can be treated as speed. you can then find acceleration from the change in speed divided by the time. go online for: links on acceleration visit: www.scilinks.org web code: ccn - 2113

Explanation:

Step1: Define the acceleration formula

Acceleration $a=\frac{v_f - v_i}{t}$, where $v_f$ is final velocity, $v_i$ is initial velocity and $t$ is time.

Step2: Understand positive and negative acceleration

If $v_f>v_i$, $v_f - v_i>0$, so $a>0$ (positive acceleration). If $v_f < v_i$, $v_f - v_i<0$, so $a < 0$ (negative acceleration).

Step3: Note vector - nature of velocity and acceleration

Velocity and acceleration are vector quantities. Even if speed is constant, change in direction means acceleration (e.g., car rounding a curve). For straight - line motion, velocity can be treated as speed for acceleration calculation.

Answer:

Acceleration is calculated as the change in velocity divided by the total time, $a = \frac{v_f - v_i}{t}$, and it can be positive or negative depending on whether velocity increases or decreases. Also, acceleration can occur due to a change in direction even when speed is constant.