Answer:
The x-coordinate of the particle is 24 m.
Explanation:
In order to obtain the x-coordinate of the particle, you have to apply the equations for Two Dimension Motion
Xf=Xo+Voxt+0.5axt²(I)
Yf=Yo+Voyt+0.5ayt² (II)
Where Xo, Yo are the initial positions, Xf and Yf are the final positions, Vox and Voy are the initial velocities, ax and ay are the accerelations in x and y directions, t is the time.
The particle starts from rest from the origin, therefore:
Vox=Voy=0
Xo=Yo=0
Replacing Yf=12, Yo=0 and Voy=0 in (I) and solving for t:
12=0+(0)t+ 0.5(1.0)t²
12=0.5t²
Dividing by 0.5 and extracting thr squareroot both sides:
t=√12/0.5
t=√24 = 2√6
Replacing t=2√6, ax=2.0,Xo=0 and Vox=0 in (I) to obain the x-coordinate:
Xf=0+0t+0.5(2.0)(2√6)²
Xf= 24 m
A truck was traveling at 16.6 miles per second and accelerates at a rate of 2.0 meters per second squared then time is required for the truck to reach a speed of 25 miles per second is 6759 s.
Explanation:
Velocity is defined as the rate of change in displacement while acceleration is defined as the rate of change of velocity. Acceleration may be positive or negative. Acceleration is positive when the velocity of the object is increases and it is negative when velocity of the object is decreases. Negative acceleration is also called deceleration.
Mathematically
a = 
Where a is the acceleration of the object,
is the final velocity of the object and
is the initial velocity of the object. t is equal to time taken.
Given data:
= 25 miles/s
= 16.6 miles/s
a = 2.0 m/s²
t = ?
As velocities and acceleration given in different units, So we need to convert to obtain same units. Here we convert unit of acceleration from m/s² to miles/s².
1 m/s² = 0.000621371192 miles/s²
2 m/s² = 0.00124274238 miles/s²
So,
a = 0.00124274238 miles/s²
Apply formula
a =
t = 
t = 
t = 6759 s
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Answer:
Part(a): The frequency is
.
Part(b): The speed of the wave is
.
Explanation:
Given:
The distance between the crests of the wave,
.
The time required for the wave to laps against the pier, 
The distance between any two crests of a wave is known as the wavelength of the wave. So the wavelength of the wave is
.
Also, the time required for the wave for each laps is the time period of oscillation and it is given by
.
Part(a):
The relation between the frequency and time period is given by

Substituting the value of
in equation (1), we have

Part(b):
The relation between the velocity of a wave to its frequency is given by

Substituting the value of
and
in equation (2), we have

In the above case we can say that power given by external agent to pull the rod must be equal to the power dissipated in the form of heat due to magnetic induction.
Part a)
when we pull the rod with constant speed then power required will be product of force and velocity
here we will have

P = 4 W
v = 4 m/s
now we will have


So external force required will be 1 N
PART B)
now in order to find magnetic field strength we can say

here we know that induced EMF in the wire is E = vBL
so power due to induced magnetic field is given by


by solving above equation we will have
