Question

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

Answer 1

Given:

`d=-gt^2+vt+c`

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

Step 1:

Subtract c from both sides

`\begin{gathered} d-c=-gt^2+vt+c-c \\ \\ d-c=-gt^2+vt \end{gathered}`

Step 2:

Divide through by t:

`\begin{gathered} (d)/(t)-(c)/(t)=(-gt^2)/(t)+(vt)/(t) \\ \\ \\ (d)/(t)-(c)/(t)=-gt+v \end{gathered}`

Step 3:

Add gt to both sides

`\begin{gathered} (d)/(t)-(c)/(t)+gt=-gt+gt+v \\ \\ (d)/(t)-(c)/(t)+gt=v \\ \\ v=(d)/(t)-(c)/(t)+gt \end{gathered}`

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

`v\text{ = }(d)/(t)-(c)/(t)+gt`

ANSWER:

`v=(d)/(t)-(c)/(t)+gt`