Answer :
Final answer:
Using the kinematic equation for uniformly accelerated motion, the correct stopping distance for a car decelerating at -6.8 m/s² from an initial speed of 36.6 m/s is 98.5 meters, which does not match any of the provided options.
Explanation:
To calculate the distance a car will travel before coming to a stop when it is decelerating, we use the kinematic equation for uniformly accelerated motion, which is:
d = v^2 / (2a)
Here, d represents the distance, v is the initial velocity, and a is the acceleration (deceleration, in this case, so it will be a negative value).
According to the problem:
- Initial velocity v = 36.6 m/s
- Deceleration a = -6.8 m/s²
Plugging these values into the equation gives us:
d = (36.6 m/s)^2 / (2 × -6.8 m/s²)
d = 1339.56 m^2/s^2 / (-13.6 m/s²)
d = -98.5 m
Since distance cannot be negative in this context, we take the absolute value which gives us:
d = 98.5 m
None of the provided options match the calculated result. Therefore, the correct stopping distance, using the given initial speed and deceleration rate, is 98.5 meters.
