Displacement equals the original velocity multiplied by time plus one half the acceleration multiplied by the square of time. Here is a sample problem and its solution showing the use of this equation: An object is moving with a velocity of 5.0 m/s.. Displacement = (final position) - (initial position) = change in position.
question answered by
(jacemorris04)
Answer:
The unit is usually seconds. But it really depends on the situation you are in. If you are talking about uranium-238, then you'll be talking about a half life in the billions of years. However, if you are talking about the half-life of a muon, then it'll be in seconds or microseconds.
Answer:
The period of the wave does not change looting the value that accompanies the time, the wavelength does not change since it is the constant that accompanies x.
We see that the amplitude is twice the amplitude of the incident waves. Since the wave is stationary the velocity is zero
Explanation:
In this exercise we are given the equation of two traveling waves, it is asked to find the resulting wave
u = f + g
u = 2 sin (x + t) + 2 sin (x-t)
we will develop double angled breasts
u = 2 [(sin x cos t + sin t cos x) + (sin x cos t - sin t cos x)]
u = 2 [2 sin x cos t]
u = 4 sin x cos t
The period of the wave does not change looting the value that accompanies the time, the wavelength does not change since it is the constant that accompanies x.
We see that the amplitude is twice the amplitude of the incident waves. Since the wave is stationary the velocity is zero
Answer:
x(t) = d*cos ( wt )
w = √(k/m)
Explanation:
Given:-
- The mass of block = m
- The spring constant = k
- The initial displacement = xi = d
Find:-
- The expression for displacement (x) as function of time (t).
Solution:-
- Consider the block as system which is initially displaced with amount (x = d) to left and then released from rest over a frictionless surface and undergoes SHM. There is only one force acting on the block i.e restoring force of the spring F = -kx in opposite direction to the motion.
- We apply the Newton's equation of motion in horizontal direction.
F = ma
-kx = ma
-kx = mx''
mx'' + kx = 0
- Solve the Auxiliary equation for the ODE above:
ms^2 + k = 0
s^2 + (k/m) = 0
s = +/- √(k/m) i = +/- w i
- The complementary solution for complex roots is:
x(t) = [ A*cos ( wt ) + B*sin ( wt ) ]
- The given initial conditions are:
x(0) = d
d = [ A*cos ( 0 ) + B*sin ( 0 ) ]
d = A
x'(0) = 0
x'(t) = -Aw*sin (wt) + Bw*cos(wt)
0 = -Aw*sin (0) + Bw*cos(0)
B = 0
- The required displacement-time relationship for SHM:
x(t) = d*cos ( wt )
w = √(k/m)
