a particle vibrates according to the equation x= 20cos(16t) where x is in centimeters. determine the amplitude and frequency of the oscillation and also the position when the kinetic energy is at a maximum.

a. A=20 cm, f=5.1 Hz, x=20 cm
b. a= 20 cm, f= 2.5 Hz, x= 20 cm
c. A=20 cm, f= 2.5 Hz, x= 0 cm
d. A= 20 cm, f= 16 Hz , x=0 cm
e. the correct information is not listed in the answer selection.
I choose b. Is that correct.

9 answers

A = 20 cm, given
when is 16 t = 2 pi ?
T = 2 *3.14159 / 16 = 0.3927 seconds period
f = 1/T = 2.55 Hz
velocity, v = -16*20 * sin 16 t
when is it max absolute value?
when 16 t = pi/2
t = 0.0982
x = 20 cos 16 * pi/32 = 20 cos pi/2 (which we should have seen before bothering to calculate v)
x= 20
so I pick B

A 1500 kg truck traveling at 80 km/h collides with another car of mass 1000 kg traveling at 30 km/h in the opposite direction. The two cars stick together after the collision. The speed immediately after the collision is

Now we have to worry about momentum, same before and after.
before:
1500 kg * 80 km/h - 1000 * 30 = 120,000 - 30,000 = 90,000 kg km/h
same after so
90,000 = (1500 +1000) v
v = 90,000 / 2500 = 36 km/h

Note - did not bother to convert km/h to m/s because the conversion cancels out
it is 1000 m / 3600 s = 1 km/ h for future reference

So it's 36 km/h

It is wise to put new questions in as new questions, not in old thread..

yes

Ok but was a correct

36 is correct

Yes, 36 is A