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?

Answer 1

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

Step-by-step 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=(dx)/(dt)\\\\v=(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=(dv)/(dt)\\\\a=(d(6.5-6.9t^2))/(dt)\\\\a=-13.8t`

Put t = 0.971 s

`a=-13.8* 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.