I don't know what to do in this problem

[elton_fan]

the problem is
a sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 3.8 m/s². after achieving top speed . he runs the remainder of the race without speeding up or slowing down. the total race is 50 meters long. if the total race is run in 7.88s how far does he run during acceleration phase.



the problem is all the equations that i have found are composed of two unknowns so i couldn't solve the problem please help me

 

[AngeloG]

Acceleration is change in velocity correct?

Once he achieves top speed and doesn't speed up or slow down. What happens to his acceleration or what is it?

Please type out all your knowns and unknowns, and an idea of how you would solve it or what you would be solving for. After that, we can help you further =).

 

[andrevdh]

Lets call the distance he covers during acceleration $$x_a$$ and the distance he covers with no acceleration (at top speed) $$x_t$$. then we have that

$$x_a + x_t = 50 m$$

the same approach with time:

$$t_a + t_t = 7.88 s$$

Use your kinematic equations to solve for $$x_a$$.

 

[andrevdh]

Can you set up equations for $$x_a$$ and $$x_t$$?

 

[AngeloG]

The x (final) you are solving for will be (50 - x) correct? Since he's running an x amount from 50. Essentially just using algebra for your xa + xt = 50 m. And your t for the interval will be t = 7.88 - t. Correct? However, you have to think what is relevant and what isn't =).

I will give you the equations, but you tell me what you would use and how you would kind of use them.

Remember, look at your knowns and unknowns and pick a good one that suits your situation =).

v = vo + at
x = xo + volt + 1/2at^2
v^2 = vo^2 + 2a(x - xo)

 

[andrevdh]

To avoid confusion I used subscripts $$a$$ to indicate a kinematic quantity that associates with the part where the athlete accelerates and $$t$$ for the part where he/she runs at top speed.