At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.70 m/s2. 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) number entry field with correct answer 53.51851852 units entry field with correct answer

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Mathematics

31 July, 11:26

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.70 m/s2. 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) number entry field with correct answer 53.51851852 units entry field with correct answer

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Francis Escobar · Answer 1

You know that t=0 and x=0, the car starts moving with a constant acceleration of 2.70m/s²

At the same time, a truck moving speed o 8.50 m/s passes the car

D=v. t (for the truck)

And d = v. t+1/2. a. t² (for the car)

v. t=1/2. a. t²

t=2. v/a

t=2.8.50 m/s / 2.70 m/s²

17m/2.70=6.29

This mean that the distance is

D=v. t=8.50m/s. 6.29 = 53.465 m/s

The speed of the car is

Vcar=a. t

2.7m/s2* * 53.65

=144.34