Question

Arrange the equations in the correct sequence to rewrite the formula for displacement, d = vt—1/2at^2 to find a. In the formula, d is
displacement, v is final velocity, a is acceleration, and t is time.

Answer 1

Answer:

$a = \frac{2(vt-d)}{t^{2} }$

Step-by-step explanation:

Given the formula for calculating the displacement of a body as shown below;

$d = vt - \frac{1}{2} at^{2}$

d = displacement

v = final velocity

a = acceleration

t = time

To make the acceleration a the subject of the formula, the followin steps must be taken;

Step 1: Subtract vt from both sides of the equation

$d-vt = vt-vt-\frac{1}{2}at^{2} \\ d-vt = -\frac{1}{2}at^{2}\\2(d-vt) = -at^{2}$

Step 2: Divide both sides by t²

$\frac{2(d-vt)}{t^{2} } = \frac{-at^{2} }{t^{2} } \\a = \frac{-2(d-vt)}{t^{2} }$

$a = \frac{2(vt-d)}{t^{2} }$