The position function of a freight train is given by s(t) = 100(t + 1)^-2, with s in meters and t in seconds. At time t = 6 s, find the train's velocity and acceleration. Using a. and b. is the train speeding up or slowing down?
Answers
Answer:
The position function of a freight train is given by s(t) = 100(t + 1)^-2, with s in meters and t in seconds. At time t = 6 s, find the train's velocity and acceleration. Using a. and b. is the train speeding up or slowing down?
Answer:
The acceleration is positive, the educate is dashing up at t = 6 s.
Step-by-step explanation:
From the above question,
To discover the pace and acceleration of the train, we want to take the first and 2d derivatives of the function function, respectively.
a. Velocity:
The pace characteristic is the by-product of the role characteristic with recognize to time:
v(t) = s'(t) = -200(t+1)^-3
At t = 6 s, the speed of the teach is:
v(6) = -200(6+1)^-3 = -2.041 m/s (rounded to three decimal places)
b. Acceleration:
The acceleration characteristic is the 2nd by-product of the role characteristic with appreciate to time:
a(t) = s''(t) = 600(t+1)^-4
At t = 6 s, the acceleration of the teach is:
a(6) = 600(6+1)^-4 = 0.255 m/s^2 (rounded to three decimal places)
Since ,
The acceleration is positive, the educate is dashing up at t = 6 s.
For more such related questions : https://brainly.in/question/35894240
#SPJ2