A personne walking at a speed of 1.7m/s see's a stoped bus 25m from him. At this moment this person starts to run with an acceleration of 1,3m/s2. After 4 secondes this personne has reached his maximum speed et it stays constant, but at the same time the bus starts moving and accelerates 2,6m/s2.

Does this person suceed in catching the bus? If so, at what time and at what distance, if not what was the smallest distance between the person and the bus.

- Im sorry if there any mistakes, i translated from french.

Ive got this so far:

Alright well, by using the initiale speed of 1,7m/s and 4s, i found his constante speed of 6.9m/s. So after that i used the acceleration and his speed to determine the distance he travelled, 17,2m. i subtracted 17,2m from 25m, which left 7,8m between the bus and the person. Then im stuck, how do i incorporate both speeds in one equations to see if he caught the bus or not?

The have to get to the same point, which is 25m further for the person.

distance= 25+ 1.7*time + 1/2 1.3 * 4^2 + max speed*(time-4)
max speed= 1.7 + 1.3*4 so put that in the first equation for max speed.
and distance= 1/2 *2.6* (t-4)^2

set these two distances equal, then solve for time. If time is real, and positive, the person catches the bus.

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