Constant Acceleration of jogging Problem

[JRangel42]

Homework Statement

Al and Bert are jogging side by side on a trail in the woods at a speed of 0.75 m/s. Suddenly, Al sees the end of the trail 35 m ahead and decides to speed up to reach it. He accelerates at constant rate of 50 m/(s^2) while Bert continues on at a constant speed. (a) How long does it take Al to reach the end of the hill?


Part (a) is the one I'm having trouble understanding.

Homework Equations

Δx = (1/2)at^2 + Vt + X

The Attempt at a Solution

35 = (1/2)(0.50)t^2 + (0.75)t
35 = (0.25)t^2 + (0.75)t
35 = t[(0.25)t + 0.75]
35/t = (0.25)t + 0.75

And, that is where I stopped. I'm sure I pretty much went wrong at the third step.

 

[PeterO]

Homework Statement

Al and Bert are jogging side by side on a trail in the woods at a speed of 0.75 m/s. Suddenly, Al sees the end of the trail 35 m ahead and decides to speed up to reach it. He accelerates at constant rate of 50 m/(s^2) while Bert continues on at a constant speed. (a) How long does it take Al to reach the end of the hill?


Part (a) is the one I'm having trouble understanding.

Homework Equations

Δx = (1/2)at^2 + Vt + X

The Attempt at a Solution

35 = (1/2)(0.50)t^2 + (0.75)t
35 = (0.25)t^2 + (0.75)t
35 = t[(0.25)t + 0.75]
35/t = (0.25)t + 0.75

And, that is where I stopped. I'm sure I pretty much went wrong at the third step.

Your summation is correct.

To solve a quadratic equation, you re-arrange to make the rhs zero, then solve by either factorisation [if you are lucky] or use the quadratic formula.

 

[technician]

Are you sure of the question wording?...you have an acceleration of 50m/s^2
Which is not realistic.
In your calculation you have 0.5 which is more realistic

 

[JRangel42]

Holy crap, I forgot about the quadratic formula. Thanks for the help.