To calculate the change in position of an object that accelerates at a constant rate, you can use the following equation:
Δx = v_i * t + 0.5 * a * t^2
Where: Δx is the change in position (displacement) of the object v_i is the initial velocity of the object t is the time interval a is the constant acceleration of the object
Let's break down each term:
v_i * t: This term represents the distance covered by the object during the initial velocity period. It is calculated by multiplying the initial velocity (v_i) by the time interval (t).
0.5 * a * t^2: This term represents the distance covered by the object due to the acceleration. It is calculated by multiplying half of the acceleration (0.5 * a) by the square of the time interval (t^2).
By summing up the two terms, you obtain the total change in position (displacement) of the object (Δx).
It's important to note that this equation assumes that the acceleration is constant throughout the time interval. If the acceleration is not constant or varies over time, a more complex set of equations or numerical methods may be required to calculate the displacement accurately.