Final answer:
The car with an initial speed of 50 m/s will travel approximately 113.64 meters before it stops, and a car with an initial speed of 100 m/s (twice as fast) will travel approximately 454.545 meters before stopping.
Step-by-step explanation:
The question involves a race car that can slow down with a constant deceleration. To find out how many meters the car will travel before it stops when moving at an initial speed of 50 m/s, we can use the kinematic equation for motion with constant acceleration, which is v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Since the car is coming to a stop, v will be 0 m/s, and the acceleration a is given as -11 m/s^2 (the negative sign indicates deceleration).
For the initial speed of 50 m/s:
- 0 = (50^2) + (2 * (-11) * s)
- s = 50^2 / (2 * 11)
- s = 2500 / 22
- s = 113.64 m (approximately)
For a car going twice as fast, or 100 m/s:
- 0 = (100^2) + (2 * (-11) * s)
- s = 10000 / (2 * 11)
- s = 10000 / 22
- s = 454.545 m (approximately)
The car going 50 m/s will travel approximately 113.64 meters before stopping, and a car going twice as fast, 100 m/s, will travel approximately 454.545 meters.