Final answer:
Using the equations of motion and quadratic formula to solve for time, the car will travel 50 m in approximately 12.245 seconds. None of the options provided in the question match this answer, therefore the correct choice is 'Information not available'.
Step-by-step explanation:
To find out how long it will take the stuntman's car to go 50 m, we need to use the equations of motion for a body with constant acceleration. The car is decelerating, which is indicated by the negative acceleration (-2 m/s²). We can use the following equation of motion:
s = ut + ½ at²
where:
- s = distance
- u = initial speed
- a = acceleration
- t = time
Plugging in the known values:
50 m = (20 m/s)t + ½ (-2 m/s²)t²
This can be rearranged into a quadratic equation:
1 m/s²t² - 20 m/st + 50 m = 0
To find t, we can use the quadratic formula:
t = ± (square root of ((-b)² - 4ac)) / (2a)
Substituting our values in:
t = ± (square root of ((20)² - 4(1)(-50))) / (2(1))
t = ± (square root of (400 + 200)) / 2
t = ± (square root of 600) / 2
The square root of 600 is approximately 24.49, so:
t = ± 24.49 / 2
t = ± 12.245
Since time cannot be negative, the positive value is the correct answer:
t = 12.245 s
So, the correct answer for the time it will take the car to go 50 m is not provided in options A) 25 s, B) 20 s, C) 30 s, hence D) Information not available is the correct answer.