Final answer:
The stuntman's car will take 10 seconds to travel 50 meters east when accelerating at a rate of -2 m/s², given the initial velocity of 20 m/s.
Step-by-step explanation:
Calculating Time for a Car to Travel a Certain Distance with Acceleration
To determine how long it takes for the stuntman's car to travel 50 m east while accelerating at a rate of -2 m/s2, we need to use the kinematic equations of motion that relate displacement, initial velocity, acceleration, and time. Since we're given the initial velocity (vi = 20 m/s), the acceleration (a = -2 m/s2), and the displacement (d = 50 m), we can use the following equation:
d = vit + ½at2
Plugging the values into the equation, we get:
50 = 20t - (1/2)(2)t2
This simplifies to:
50 = 20t - (1)t2
Rearranging to form a quadratic equation:
t2 - 20t + 50 = 0
The above quadratic equation can be solved using the quadratic formula or factoring. Solving for t yields:
t = 5 s or t = 10 s
The negative root is discarded since time cannot be negative. Therefore, the correct answer is B. 10 s.