A small mass sliding on a certain inclined plane is subject to an acceleration downward along the plane of $4$ feet per second. If it started upward from the bottom of the incline with a velocity of $6$ feet per second, then find the distance it moves in $t$ seconds. How far will it go before stopping and starting to slide back?
2026-04-28 18:45:38.1777401938
Calculus for the Practical Man: Chapter 17, Problem 6
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"In a way, this post seems perfectly reasonable. I believe this is how many "practical men" would solve this problem." John Douma
Am I missing something? This appears to be a response to a solution but I see no solution!
In addition, this problem states that the acceleration is "4 feet per second" but "feet per second" is NOT a measure of acceleration!
If -4 feet per second per second was meant (negative since it is back toward the ground) then, with a starting speed of 6 feet per second, then, after t seconds this object will have speed 6- 4t feet per second and will have gone 6t- 2t^2 feet.
The object will stop and turn back when its speed is 0 so when 6- 4t= 0. 4t= 6 so t= 6/4= 3/2 second. At that time it will have gone up the slope 6(3/2)- 2(9/4)= 18/2- 9/2= 9/2 or 4.5 feet.