Question

Physics/Algebra Question really needed Number 32 C!!!

Answer 1

If
`d_t=d_f`, then

`d_t=d_f+v_0t+\frac12at^2\implies0=v_0t+\frac12at^2`

We can factor out
`\frac12t` to write

`\frac12t(2v_0+at)=0`

which means that either
`t=0` or
`2v_0+at=0`. In the latter case, we can directly solve for
`t` to get

`2v_0+at=0\implies at=-2v_0\implies t=-\frac{2v_0}a`