Question

In the particle under constant acceleration model, we identify the variables and parameters Vxi, Vxf, ax, t, and xf-xi. Of the equations in the model, Equations 2.13-2.17, the first does not involve xf-x, the second and third do not contain ax, the fourth omits Vxf, and the last leaves out t. So, to complete the set, there should be an equation not involving Vxi. Derive it from the others.

a) Vxf=Vxi+at
b) xf−xi=1/2(Vxi+Vxf)t
c) V²xf=V²xi+2a(xf−xi)
d) xf−xi=Vxit+21at²

Answer 1

Equation (d) is the equation that does not involve the initial velocity (Vxi) in the particle under the constant acceleration model. It can be derived from the other equations by substituting equation a (Vxf = Vxi + at) into equation b (xf - xi = 1/2(Vxi + Vxf)t) and simplifying.

Step-by-step explanation:

Equation (d) is the equation that does not involve the initial velocity (Vxi) in the particle under the constant acceleration model. To derive it from the other equations, we can start with the equation xf - xi = 1/2(Vxi + Vxf)t (equation b). Rearranging this equation, we get xf - xi = (Vxi + Vxf)t/2. Now, substituting equation a (Vxf = Vxi + at) into this equation, we have xf - xi = (Vxi + (Vxi + at))t/2. Simplifying further gives xf - xi = (2Vxi + at)t/2 = Vxit + (1/2)at². This derived equation (d) represents displacement purely in terms of time (t), initial velocity (Vxi), and acceleration (a) without relying on the final velocity, showcasing an alternative perspective in calculating displacement under constant acceleration.