The velocity of a particle constrained to move along the x-axis as a function of time t is given by: v(t)=-(15/t_0) sin(t/t_0). a)if the particle is at x=4 m when t = 0, what is its position at t = 4t_0. you will not need the value of t_0 to solve any part of this problem. b)denote instantaneous acceleration of this particle by a(t). evaluate the expression 6 + v(0) t + a(0) t^2/2 at t = 4t_0.

The answer is:

v = 15/T sin t/T 

then integrate 

x = -15 cos t/T + c 

if x = 4 at t = 0 then 

4 = -15 + c so c = 19 

so 

x = 19 - 15 cos t/T 

at t = 4T 

x = 19 - 15 cos 4 = 3.99 or 4

b) 

a = dv/dt = 15/T^2 cos t/T 

v(0) = 0 since sin 0/T = 0 

a(0) = 15/T^2 

so 

6 + 0 +(7.5/T^2) (16 T^2) 

= 6 + 7.5*16

= 126 is the answer 

that tool is called an altimeter which measures your altitude which can be used to tell which atmosphere you are currently in, including the stratosphere.

hope this ! : )