A motorist drives along a straight road at a constant speed of 15.0 m/s. Just as she passes a parked motorcycle police offi cer, the offi cer starts to accelerate at 2.00 m/s2 to overtake her. Assuming that the offi cer maintains this acceleration, (a) determine the time interval required for the police offi cer to reach the motorist. Find (b) the speed and (c) the total displacement of the offi cer as he overtakes the motorist.
Answers
Answer:
a) The time the police officer required to reach the motorist was 15 s.
b) The speed of the officer at the moment she overtakes the motorist is 30 m/s
c) The total distance traveled by the officer was 225 m.
Explanation:
The equations for the position and velocity of an object moving in a straight line are as follows:
x = x0 + v0 · t + 1/2 · a · t²
v = v0 + a · t
Where:
x = position at time t
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
v = velocity at time t
a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:
x motorist = x officer
Using the equation for the position:
x motirist = x0 + v · t (since a = 0).
x officer = x0 + v0 · t + 1/2 · a · t²
Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:
x motorist = x officer
x0 + v · t = x0 + v0 · t + 1/2 · a · t² (the officer starts form rest, then, v0 = 0)
v · t = 1/2 · a · t²
Solving for t:
2 v/a = t
t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s
The time the police officer required to reach the motorist was 15 s.
b) Now, we can calculate the speed of the officer using the time calculated in a) and the equation for velocity:
v = v0 + a · t
v = 0 m/s + 2.00 m/s² · 15 s
v = 30 m/s
The speed of the officer at the moment she overtakes the motorist is 30 m/s
c) Using the equation for the position, we can find the traveled distance in 15 s:
x = x0 + v0 · t + 1/2 · a · t²
x = 1/2 · 2.00 m/s² · (15s)² = 225 m
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When only "bulb a" is connected to the battery then more current is flowing to "bulb a" causing it to be bright.
Closing the switch would mean that "bulb b" is already included in the circuit and the battery will push small current to flow around the whole circuit. The more bulbs are connected, the harder for the current to flow because the resistance will be very high.
So the light of "bulb a" will be dimmer.
There is a pattern of current flow. Based on the above scenario, Option b is the correct answer as bulb B will be brighter than before (Image attached).
What does this implies?Based on the current flowing through bulb A is said to remains the same in both scenario. It is the current through bulb B that changes when the switch are said to be closed.
There is something that happens to the brightness of a bulb when the switch is said to be closed. Note that when the switch is closed, the light bulb often operates because of the current flows via the circuit. The bulb (B) tends to glows at its full brightness because it receives more volts.
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Particles in which state are close together, yet free to move around one another?
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It is important to note that large-scale maps, like a standard topographic map, typically have less distance distortion, making it easier to measure straight line distances. However, when measuring distances along curved features, techniques such as using multiple straight-line segments or tools like an opisometer may be employed for greater accuracy. Map scales can be complex, as they can vary with latitude due to the Earth's curvature, particularly on maps that cover large areas such as equidistant projections which are true-to-scale only along meridians.
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A constant force of f = 47i + 30j moves an object along a vector d = 13i - 8j, where units are in pounds and feet. find the work done.
Answers
Answer:
The work is 371 lb ft
Explanation:
The work can be calculated with yhe scalar product between the force and the displacement:
[tex] W = F.d [/tex]
The scalar product is obtained multiplying component to comoponent and summing the terms:
[tex] W [/tex] = <47, 30> · <13, -8> [lb ft]
[tex] W [/tex] = 47*13 + 30*(-8) [lb ft]
Finally:
W = 371 [lb ft]