To find the car's final velocity, we can use the kinematic equation:
v_f = v_i + at
Where: v_f = final velocity v_i = initial velocity a = acceleration t = time
In this case, the car's initial velocity is 15.0 m/s, and the time is given as 0.50 min, which we need to convert to seconds:
t = 0.50 min × 60 s/min = 30 s
The car's acceleration can be calculated using the formula:
a = (v_f - v_i) / t
Rearranging the formula, we have:
v_f = v_i + at
We have the values for v_i and t, and we need to find the value for a. To do that, we'll use the equation that relates distance, acceleration, initial velocity, and time:
d = v_i * t + (1/2) * a * t^2
Rearranging this equation, we get:
a = (2 * (d - v_i * t)) / t^2
Plugging in the values we know:
d = 650 m v_i = 15.0 m/s t = 30 s
a = (2 * (650 m - 15.0 m/s * 30 s)) / (30 s)^2
Simplifying this expression, we get:
a = (2 * (650 m - 450 m)) / 900 s^2 a = (2 * 200 m) / 900 s^2 a = 400 m / 900 s^2 a ≈ 0.444 m/s^2
Now that we have the acceleration value, we can calculate the final velocity using the first equation:
v_f = v_i + at
v_f = 15.0 m/s + 0.444 m/s^2 * 30 s v_f = 15.0 m/s + 13.332 m/s v_f ≈ 28.332 m/s
Therefore, the car's final velocity is approximately 28.332 m/s.