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alexandr1967 [171]
3 years ago
9

A video game includes an asteroid that is programmed to move in a straight line across a 17-inch monitor according to the equati

on 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?
Physics
1 answer:
Ainat [17]3 years ago
6 0

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.

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