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d = -gt^2 + vt + c. the equation expresses the distance, d, in feet, of a ball t seconds after it is thrown straight up with an initial velocity of v feet per second and from a starting point of c feet. which of the following expresses v in terms of d, g, t, and c? A) v = d - c - + g/t B) v = d + c + g/t C) v = d + c/t - gt D) v = d - c/t + gt

Respuesta :

Given:

[tex]d=-gt^2+vt+c[/tex]

To express v in terms of d, g, t, and c, take the following steps:

Step 1:

Subtract c from both sides

[tex]\begin{gathered} d-c=-gt^2+vt+c-c \\ \\ d-c=-gt^2+vt \end{gathered}[/tex]

Step 2:

Divide through by t:

[tex]\begin{gathered} \frac{d}{t}-\frac{c}{t}=\frac{-gt^2}{t}+\frac{vt}{t} \\ \\ \\ \frac{d}{t}-\frac{c}{t}=-gt+v \end{gathered}[/tex]

Step 3:

Add gt to both sides

[tex]\begin{gathered} \frac{d}{t}-\frac{c}{t}+gt=-gt+gt+v \\ \\ \frac{d}{t}-\frac{c}{t}+gt=v \\ \\ v=\frac{d}{t}-\frac{c}{t}+gt \end{gathered}[/tex]

Therefore, the expression of v in terms of d, g, and c is:

[tex]v\text{ = }\frac{d}{t}-\frac{c}{t}+gt[/tex]

ANSWER:

[tex]v=\frac{d}{t}-\frac{c}{t}+gt[/tex]

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