At the instant a traffic light turns green, a car that has been waiting at the intersection starts moving with a constant acceleration of 2.5 m/s/s. At that moment a truck traveling with a constant velocity of 15.0 m/s is at the same position along the road and passes the car in the next lane. Calculate the distance beyond the traffic light where the car and the truck will be side-by-side.

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whitneytr12 whitneytr12 · Answer 1 · 2020-09-24T02:34:06+02:00

Answer:

d = 180 m.

Explanation:

We can find the distance where the car and the truck will be side-by-side as follows:

For the car we have:

[tex] X_{f} = X_{0} + V_{0}t + \frac{1}{2}a_{c}t^{2} [/tex]

Where:

[tex]X_{f}[/tex] is the final position

[tex]X_{i}[/tex] is the initial position = 0

[tex]V_{0}[/tex] is the initial speed = 0

[tex]a_{c}[/tex]: is the acceleration = 2.5 m/s²

t: is the time

[tex] X_{f} = \frac{1}{2}a_{c}t^{2} [/tex] (1)

For the truck we have:

[tex] X_{f} = X_{0} + V_{0}t + \frac{1}{2}at^{2} [/tex]

[tex] X_{f} = 0 + V_{0}t + \frac{1}{2}0*t^{2} [/tex]

[tex] X_{f} = V_{0}t [/tex] (2)

By equating equation (1) and (2) we have:

[tex] \frac{1}{2}a_{c}t^{2} = V_{0}t [/tex]

[tex] t = \frac{2V_{0}}{a_{c}} = \frac{2*15 m/s}{2.5 m/s^{2}} = 12 s [/tex]

Since the car and the truck will be side-by-side at 12 seconds, we can calculate now the distance:

[tex] X_{f} = V_{0}t = 15 m/s*12 s = 180 m [/tex]

Therefore, the distance at which the car and the truck will be side-by-side is 180 m.

I hope it helps you!