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?

Question

contestada

Respuesta :

valeriagonzalez0213 valeriagonzalez0213 · Answer 1 · 2019-09-19T00:09:55+02:00

Answer:

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