i need to solve for t

Question

kinematic equation for physics/mechanics

d= vt + 1/2at^2

Answer 1

Set it up in the form of a quadratic equation, and then solve it using the quadratic formula. You will get two solutions, so you will need to discriminate which one is correct in the context of the problem.

d = vt + (1/2)at²

(1/2)at² + vt - d = 0

t = {-v ± √[v² - 4(a/2)(-d)]} / [2(a/2)]

SImplify, plug in the numbers, evaluate, and finish from here.

Answer 2

d = vt + 1/2*at²

This is a quadratic equation. You can re-write it in the standard quadratic form ax² + bx + c = 0. The standard quadratic equation has two potential solutions given by

x = [-b ± √(b²-4ac)]/2a

The equation of motion written in the standard quadratic form is

at² + 2vt - 2d = 0

You can get the solution for t

t = [-2v ± √(4v² + 8ad)]/2a

By re-arranging terms you can write it in a more elegant format

t = v/a*[-1 ± √(1 +2ad/v²)]

I hope this is what you were looking for. If I misread, let me know and I can try helping with your question.