The acceleration of the bike is equal to [tex]8.78\frac{m}{s^{2}}[/tex] opposing the movement (to the right).
Why?
Since after the rider slams the brakes, the bike came to a stop, we know that the acceleration is opposite to the velocity/movement.
We can use the following equation to calculate the acceleration:
[tex]v_{f}^{2}=v_{o}^{2}+2*a*d[/tex]
So, substituting, we have: (let's consider negative to the left and positive to the right)
[tex]0=(-27\frac{m}{s} )^{2}+2*a*41.5m\\\\0=729\frac{m^{2} }{s^{2} }+83*a\\\\a=\frac{-729\frac{m^{2}}{s^{2}}}{83m}=-8.78\frac{m}{s^{2}}[/tex]
The negative sign means that the acceleration's direction is opposite to the movement.
Hence, we have that the acceleration is equal to [tex]8.78\frac{m}{s^{2}}[/tex] opposing the movement (to the right).
Have a nice day!
