Question

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

v(t)=-(13/t_0) sin(t/t_0).

a)If the particle is at x=4 m when t = 0, what is its position at t = 5t_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 4 + v(0) t + a(0) t^2/2 at t = 5t_0. You will find that this does not agree with the answer to part (a), which is expected because the acceleration in this problem is changing with time.

c)Assume that the particle is at x = 0 when t = 0, and find its position at t = 0.15t_0.

d)Evaluate v(0) t + a(0) t^2/2 at t =0.15t_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)

Answer 1

a) position(t)=position(t=0)+v(t)*t

I will be happy to critique your thinking.

Answer 2

I would know how to solve this problem if i were to understand the whole t/t_0 thing. I don't know how to integrate something like that. Could you please explain how to get it started

Answer 3

There is no integration here, it is straight calculation with your calculator.

Answer 4

so i get v(t)=-(13*5)/t