At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.20 m/s^2. at the same instant a truck, traveling with a constant speed of 8.50 m/s, overtakes and passes the automobile. (a) how far beyond the traffic signal will the automobile overtake the truck? (b) how fast will the automobile be traveling at that instant?

a) d=65.7 m : The automobile overtake passes the truck at a distance of 65.7 m  from the traffic signal

b) vₐ=16.94m/s : Automobile  speed for t = 7.7s

Explanation:

When the car catches the truck, the two will have passed the same time (t) and will have traveled the same distance (d):

Automobile kinematics:

car moves with uniformly accelerated movement:

d = v₀*t + (1/2)a*t²

v₀ = 0 : initial speed  

d = (1/2)*a*t² Equation (1)

Truck kinematics:

Truck moves with constant speed:

d = v*t Equation (2)

Data:

a=2.20 m/s² : automobile acceleration

v= 8.50 m/s  ; truck speed

Equation (1) =Equation (2)

(1/2)*a*t²= v*t

(1/2)*2.2*t²= 8.5*t   We divide both sides of the equation by t:

1.1*t=8.5

t=8.5÷1.1

t=7.7 s

We replace t=7.7 s in the equation (2)

d=8.5*7.7

d=65.7 m

Automobile  speed for t = 7.7s

vₐ=v₀₊a*t

vₐ=o₊2,2*7.7

vₐ=16.94m/s

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