Question

The velocity of a particle constrained to move along the x-axis as a function of time t is given by:

v(t)v(t)=−(−(14/t0)sin(t/t0)/t0)sin(t/t0).

Part A:

If the particle is at x=8 m when t=0, what is its position at t = 9t0. You will not need the value of t0 to solve any part of this problem. If it is bothering you, feel free to set t0=1everywhere.

Part B:

Denote instantaneous acceleration of this particle by a(t). Evaluate the expression 8 +v(0)t+a(0)t2/2+v(0)t+a(0)t2/2 at t = 9t₀. Note that v(0) and a(0) are the velocity and acceleration at time t=0.

Part C:

Now assume that the particle is at x=0 when t=0, and find its position at t = 0.20t0.

Part D:

Evaluate v(0)t+a(0)t2/2v(0)t+a(0)t2/2 at t =0.20t0 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)

Answer 1