A video game includes an asteroid that is programmed to move in a straight line across a 17-inch monitor according to the equation x=6.5t−2

Question

A video game includes an asteroid that is programmed to move in a straight line across a 17-inch monitor according to the equation x=6.5t−2.3 t 3 x=6.5t−2.3t3 , where x is in inches and t is in seconds. At some point during the trip across the screen, the asteroid is at rest. What is the asteroid’s acceleration at this point?

in progress 0
Delwyn 3 years 2021-07-15T13:25:44+00:00 1 Answers 22 views 0

Answers ( )

  1. Nick
    0
    2021-07-15T13:27:14+00:00
    Reply

    Answer:

    The asteroid’s acceleration at this point is 2.71\ m/s^2

    Explanation:

    The equation that governs the trajectory of asteroid is given by :

    x=6.5t-2.3t^3

    The velocity of asteroid is given by :

    v=\dfrac{dx}{dt}\\\\v=\dfrac{d(6.5t-2.3t^3)}{dt}\\\\v=6.5-6.9t^2

    At some point during the trip across the screen, the asteroid is at rest. It means, v = 0

    So,

    6.5-6.9t^2=0\\\\t=0.971\ s                      

    Acceleration,

    a=\dfrac{dv}{dt}\\\\a=\dfrac{d(6.5-6.9t^2)}{dt}\\\\a=-13.8t                        

    Put t = 0.971 s

    a=-13.8\times 0.197\\\\a=-2.71\ m/s^2

    So, the asteroid’s acceleration at this point is 2.71\ m/s^2 and it is decelerating.

Leave an answer

Browse

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