The car starts to move at an acceleration of 1 meter per second from a standstill. At 20 meters behind the car, while the car starts to move, someone starts to catch up at a constant speed of 6 meters per second on his bicycle. Can he catch up? What is the minimum distance between people and the car?

The car starts to move at an acceleration of 1 meter per second from a standstill. At 20 meters behind the car, while the car starts to move, someone starts to catch up at a constant speed of 6 meters per second on his bicycle. Can he catch up? What is the minimum distance between people and the car?

Let t be the time to catch up
6*t-1/2at^2=20
T has no solution, so it can't catch up
When the speed is equal, the distance between two cars is the minimum
6=at
t=6s
s1=6*6=36m
s2=1/2at^2=18
Minimum distance = 20 + 18-36 = 2m