Answer to Question #225031 in Classical Mechanics for Ace

Question #225031
5.At the instant, traffic light turns green, an automobile that has been waiting at an intersection of roads accelerate with 5m/s. At the same instant a truck travelling with a constant velocity of 20m/s overtake and passes the automobile.
a.How far beyond it's starting point will the automobile overtake the truck.
b.How fast will it be travelling?
1
Expert's answer
2021-08-11T09:53:45-0400

for automobile:\text{for automobile:}

v0=0;a=5ms2v_0 =0;a= 5\frac{m}{s^2}

saut(t)=v0t+at22=5t22s_{aut}(t) = v_0t+\frac{at^2}{2}=\frac{5t^2}{2}

vaut(t)=v0+at=5tv_{aut}(t)= v_0+at = 5t

for truck:\text{for truck:}

vtr=20msv_{tr}= 20\frac{m}{s}

str(t)=vtrt=20ts_{tr}(t) = v_{tr}t= 20 t


saut=strs_{aut} = s_{tr}

5t22=20t\frac{5t^2}{2}= 20t

t1=0 this is the beginning of the movementt_1= 0 \text{ this is the beginning of the movement}

t2=8st_2 = 8s

str(t2)=20t2=160ms_{tr}(t_2) = 20 *t_2= 160m

vaut(t2)=5t2=40msv_{aut}(t_2)=5t_2= 40\frac{m}{s}


Answer: a.\text{Answer: }a.160 m b.40ms40\frac{m}{s}



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