A snowboarder starts from rest at the top

A snowboarder starts from rest at the top of a double black diamond hill. As he rides down the slope, GPS coordinates are used to determine his displacement as a function of time: x= 0.5t^3 + t^2 + 2t where x and t are expressed in ft and seconds, respectively. Determine the position, velocity, and acceleration of the boarder when t=5 seconds.



Show me the final answer↓

We can figure out the position by substituting 5 seconds into our position equation.

x= 0.5t^3 + t^2 + 2t

x= 0.5(5)^3 + (5)^2 + 2(5)=97.5 ft


To figure out the velocity, we will take the derivative of our position equation.



Again, substitute t=5 into our velocity equation to figure out the velocity at 5 seconds.


v=1.5(5)^2+2(5)+2=49.5 ft/s


To find the acceleration, we will take the derivative of the velocity equation.



As before, substitute t=5 into our acceleration equation to figure out the acceleration at 5 seconds.




Final Answers:

x=97.5 ft

v=49.5 ft/s



This question can be found in Vector Mechanics for Engineers: Statics and Dynamics, 11th edition, chapter 11, question 11.1.

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