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.

Question

Physics

Moocher

24 March, 03:03

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.

+2

Answers (1)

Know the Answer?

Destiney Buchanan · Answer 1

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