SOLUTION: a cyclist is riding along at a constant velocity of 15 m/s. He then accelerates at a uniform rate of 0.50 m/s^2 over a distance of 64 m/s. How long did he accelerates for?

Question 932600: a cyclist is riding along at a constant velocity of 15 m/s. He then accelerates at a uniform rate of 0.50 m/s^2 over a distance of 64 m/s. How long did he accelerates for?

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
use one of the big 4 kinematic equations:
d = vi*t + (1/2)*a*t^2
---
d = distance
vi = velocity initial
t = time
a = acceleration
---
64 = 15t + (1/2)*0.50*tt
64 = 15t + (1/2)*(1/2)*tt
64 = 15t + (1/4)*tt
0.25tt + 15t - 64 = 0
---
the above quadratic equation is in standard form, with a=0.25, b=15 and c=-64
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.25 15 -64
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
t = 4
t = -64
---
the negative root doesn't fit the problem statement, so use the positive root:
---
answer:
t = 4 seconds
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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