To begin, it is important to understand the concept of acceleration and how it affects motion. Acceleration is the rate of change of an object's velocity over time, and it can either be positive (speeding up) or negative (slowing down). In this scenario, Sue is driving at a constant velocity of 30m/s, meaning she is not accelerating. However, when she applies her brakes, she will experience a negative acceleration of -2.00m/s^2.
Next, we need to determine the distance and time it will take for Sue to come to a stop. Using the equation d = vi * t + (1/2) * a * t^2, where d is the distance, vi is the initial velocity, a is the acceleration, and t is the time, we can plug in the values given in the scenario. Sue's initial velocity is 30m/s, and her acceleration is -2.00m/s^2. We do not know the time, so we can leave it as t. The distance, d, is the sum of the distance between Sue and the van (155m) and the distance it takes for Sue to come to a stop. Therefore, the equation becomes 155m = 30m/s * t + (1/2) * (-2.00m/s^2) * t^2.
To solve for t, we can rearrange the equation to t^2 - 15t + 155 = 0. Using the quadratic formula, we find that t = 13.63 seconds. This means it will take Sue 13.63 seconds to come to a stop after applying her brakes.
Now, we can determine if there will be a collision. In that 13.63 seconds, the van will have traveled a distance of (5m/s * 13.63s) = 68.15m. This means that when Sue comes to a stop, she will have traveled a distance of (30m/s * 13.63s) = 408.9m. Since the van will only be 68.15m ahead of Sue, there will not be a collision.
In conclusion, by using the equation for distance and understanding the concept of acceleration, we can determine that there will not be a collision between Sue and the slow-moving van. However, it is important for Sue to always maintain a safe distance from other vehicles and to
