. (a) How far will Carlos travel before he catches up to Miko? (b) What is Carlos’ speed at this point?

Question

1. Carlos is sitting in his car at a red stoplight. As soon as the light turns green Carlos begins to accelerate at 2.2 m/s2. At the same time Miko drives past Carlos traveling at a constant 9.5 m/s. (a) How far will Carlos travel before he catches up to Miko? (b) What is Carlos’ speed at this point?

Answer 1

9.5t = 0.5*2.2*t^2
or t =9.5/1.1 = 8.64 s

So, distance travelled = 9.5*8.64 m = 82.08 m

Speed = 2.2*8.64 = 19.008 m/s

Answer 2

Carlos begins moving at zero starting speed and acceleration a=2.2m/s*2. His speed will grow as Vcarlos=aT=2.2T(m/s*2). His way that he will travel from zero time to time T will be as the following: S=(1/2)aT*2 (one half of the acceleration multiplied by time in second degree).
The way that Miko travels depends on his velocity, which is unchanged: Smiko=VmikoT

We have to solve the equation and to find the moment of time T when the way travelled by Miko is equal to the way travelled by Carlos.
VmicoT=(1/2)a(T*2).
Let us divide both sides of the equation by T:
we obtain Vmico=(1/2)aT
hence T=2Vmico/a=19(m/s)/2.2(m/s*2)=
=19/2.2(s)=8.6(36)s
The way is S=(1/2)aT*2=VmikoT=
=9.5(m/s)8.6(36)=82.0(45)m (this is the answer)
Carlos' speed at the moment is
Vcarlos =aT=2.2(m/s*2)8.6(36)s=19m/s, (this is the answer),
that is his speed at the moment he catches up Miko is twice that of Miko, as we obtained previously.