Answer:
Yes, there is a collision
Explanation:
Sue decelerates at a constant rate, so we can use kinematic equations, also known as SUVAT equations, to model her motion. In this case, we will use two equations:
v = u + at
v² = u² + 2as
where
In this case, u = 32.0 m/s, v = 5.50 m/s, and a = -1.60 m/s². Use the equations to find the time it takes and the distance traveled for Sue to match the van's speed.
v = u + at
5.50 = 32.0 + (-1.60) t
t = 16.56 s
v² = u² + 2as
(5.50)² = (32.0)² + 2 (-1.60) s
s = 311 m
Now check how far the van travels during that time.
(5.50 m/s) (16.56 s) = 91.09 m
The van was originally 160 m in front of Sue, so by the time she slows down, the van's position will be 160 + 91 = 251 meters from Sue's starting point.
Sue's position will be at 311 meters, and the van's position will be at 251 meters. Therefore, Sue will hit the van before reaching the van's speed.
