Question
The position of a toy locomotive mobing on a straight track along the x-axis is given the equation x=t^3-6t^2 +9t where x is in metters and t is in seconds. The net force on the locomotive is equal to zero when t is eqaul to
a) zero
b)2 s
c)3 s
d)4s
e)5s
Would the answer be b)2 s? I found the double derivative of the equation and set x to 0 and solved for t.
f'= 3t^2 - 12t + 9
f"=6t - 12
yes, t=2
a) zero
b)2 s
c)3 s
d)4s
e)5s
Would the answer be b)2 s? I found the double derivative of the equation and set x to 0 and solved for t.
f'= 3t^2 - 12t + 9
f"=6t - 12
yes, t=2
Answers
Yes, you are correct. The answer is b) 2 s.
You found the double derivative (acceleration) of the position function and set it to zero, which is the condition for the net force to be zero (F = ma, and F = 0 when a = 0). From there, you solved for t and found t=2, which corresponds to option b.
You found the double derivative (acceleration) of the position function and set it to zero, which is the condition for the net force to be zero (F = ma, and F = 0 when a = 0). From there, you solved for t and found t=2, which corresponds to option b.