Final answer:
To solve for time t, we use the known values of initial velocity, acceleration, and displacement in the kinematic equation x = xo + vot + 1/2at². The result is a quadratic equation that we solve to find the value(s) of time t.
Step-by-step explanation:
To solve for the time t, we must use an equation that relates the variables we know: initial velocity vo, acceleration a, and displacement x. The question presents the knowns as vo = 10 m/s, a = 2.00 m/s², and x = 200 m. The equation that fits this scenario is x = xo + vot + 1/2at². Our goal is to find t.
Given the equation and known values, we substitute and rearrange to find t as follows:
- Substitute known values into the equation: 200 m = 0 m + (10.0 m/s)t + (1/2)(2.00 m/s²)t²
- Simplify the equation: 200 m = 10t + t²
- Rearrange the quadratic equation to solve for t: 0 = t² + 10t - 200
- Solve the quadratic equation using the quadratic formula or other methods to find the value(s) of t.
Upon solving this equation, we can determine the unknown time t.