The velocity of a particle constrained to move along the x-axis as a function of time t is given by:
v(t)=−(11/t_0)sin(t/t_0).
If the particle is at x=1 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. If it is bothering you, feel free to set t_0=1 everywhere.
Denote instantaneous acceleration of this particle by a(t). Evaluate the expression 1 +v(0)t+a(0)t^2/2 at t = 4t_0. Note that v(0) and a(0) are the velocity and acceleration at time t=0.
Now assume that the particle is atx=0when t=0, and find its position at t=0.13t_0

Question

The velocity of a particle constrained to move along the x-axis as a function of time t is given by:
v(t)=−(11/t_0)sin(t/t_0).
If the particle is at x=1 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. If it is bothering you, feel free to set t_0=1 everywhere.
Denote instantaneous acceleration of this particle by a(t). Evaluate the expression 1 +v(0)t+a(0)t^2/2 at t = 4t_0. Note that v(0) and a(0) are the velocity and acceleration at time t=0.
Now assume that the particle is atx=0when t=0, and find its position at t=0.13t_0

anonymous · Answer

Evaluate v(0)t+a(0)t^2/2 at t =0.13t_0 to 3 significant figures. Your answers to parts (c) and (d) should be in good agreement. Try to work out why that is so before submitting the answer to part (d)