Final answer:
The race car's acceleration is 17.34 m/s², calculated using the kinematic equation for motion based on the final velocity, initial velocity, and displacement.
Step-by-step explanation:
To calculate the acceleration of a race car that changes velocity from 0.0 m/s to 51.0 m/s over a displacement of 75.0 m, we can use the kinematic equation:
\(v^2 = u^2 + 2as\)
Where:
\(v\) is the final velocity (51.0 m/s)
\(u\) is the initial velocity (0.0 m/s)
\(a\) is the acceleration
\(s\) is the displacement (75.0 m)
We first rearrange the equation to solve for \(a\):
\(a = \frac{v^2 - u^2}{2s}\)
Now substituting in the values given:
\(a = \frac{51.0^2 - 0.0^2}{2*75.0}\)
\(a = \frac{2601}{150}\)
\(a = 17.34 m/s^2\)
The car's acceleration is 17.34 m/s2.