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.

Question

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.

in progress 0
Latifah 4 years 2021-07-16T03:32:16+00:00 1 Answers 16 views 0

Answers ( )

  1. thienthi
    0
    2021-07-16T03:33:44+00:00
    Reply

    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:

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

    Where:

    X_{f} is the final position

    X_{i} is the initial position = 0

    V_{0} is the initial speed = 0

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

    t: is the time  

    X_{f} = \frac{1}{2}a_{c}t^{2}   (1)

    For the truck we have:

    X_{f} = X_{0} + V_{0}t + \frac{1}{2}at^{2}

    X_{f} = 0 + V_{0}t + \frac{1}{2}0*t^{2}

    X_{f} = V_{0}t  (2)

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

    \frac{1}{2}a_{c}t^{2} = V_{0}t  

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

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

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

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

    I hope it helps you!

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )