Penny has two dogs: Fluffy (left) and Butch (right).
2 answers:
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Answer:
Refer to the attachment for the diagram.
3.53 m/s.
Explanation:
Acceleration is the first derivative of velocity relative to time. In other words, the acceleration is the same as the slope (gradient) of the velocity-time graph. Let represents the time in seconds and
the speed in meters-per-second.
For :
- Initial value of
:
at
; Hence the point on the segment:
.
- Slope of the velocity-time graph is the same as acceleration during that period of time:
.
- Find the equation of this segment in slope-point form:
.
Similarly, for :
- Initial value of
:
; Hence the point on the segment:
.
- Slope of the velocity-time graph is the same as acceleration during that period of time:
.
- Find the equation of this segment in slope-point form:
.
For :
- Initial value of
:
; Hence the point on the segment:
.
- Slope of the velocity-time graph is the same as acceleration during that period of time:
. There's no acceleration. In other words, the velocity is constant.
- Find the equation of this segment in slope-point form:
.
For :
- Initial value of
:
; Hence the point on the segment:
.
- Slope of the velocity-time graph is the same as acceleration during that period of time:
. In other words, the velocity is decreasing.
- Find the equation of this segment in slope-point form:
.
For :
- Initial value of
:
; Hence the point on the segment:
.
- Slope of the velocity-time graph is the same as acceleration during that period of time:
- Find the equation of this segment in slope-point form:
.
is in the interval
. Apply the equation for that interval:
.
(a) The net flux through the coil is zero.
In fact, the magnetic field generated by the wire forms concentric circles around the wire. The wire is placed along the diameter of the coil, so we can imagine as it divides the coil into two emisphere. Therefore, the magnetic field of the wire is perpendicular to the plane of the coil, but the direction of the field is opposite in the two emispheres. Since the two emispheres have same area, then the magnetic fluxes in the two emispheres are equal but opposite in sign, and so they cancel out when summing them together to find the net flux.
(b) If the wire passes through the center of the coil but it is perpendicular to the plane of the wire, the net flux through the coil is still zero.
In fact, the magnetic field generated by the wire forms concentric lines around the wire, so it is parallel to the plane of the coil. But the flux is equal to
where
is the angle between the direction of the magnetic field and the perpendicular to the plane of the coil, so in this case 
and so the cosine is zero, therefore the net flux is zero.
In fact, the magnetic field generated by the wire forms concentric circles around the wire. The wire is placed along the diameter of the coil, so we can imagine as it divides the coil into two emisphere. Therefore, the magnetic field of the wire is perpendicular to the plane of the coil, but the direction of the field is opposite in the two emispheres. Since the two emispheres have same area, then the magnetic fluxes in the two emispheres are equal but opposite in sign, and so they cancel out when summing them together to find the net flux.
(b) If the wire passes through the center of the coil but it is perpendicular to the plane of the wire, the net flux through the coil is still zero.
In fact, the magnetic field generated by the wire forms concentric lines around the wire, so it is parallel to the plane of the coil. But the flux is equal to
where