A powerful motorcycle can accelerate from rest to 24.8 m/s (55 mi/h) in only 5.90 s. (a) What is its average acceleration in m/s
1 answer:
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Answer:
A. The work done by the intern is 792 J.
B. The velocity of the gurney when it has moved 12 m is 6.1 m/s.
C. The 12-m journey takes 3.8 s.
Explanation:
Hi there!
Please see the attached figure for a description of the situation.
<u>Part A: </u>
Work is done by a force when it is applied in the direction of the displacement or against it. In this case, the only force applied in the direction of displacement is the horizontal component of the force applied by the intern.
By trigonometry, the horizontal component of the force is calculated as follows:
cos θ = adjacent/hypotenuse
Looking at the figure, you can notice that the applied force, F, is the hypotenuse of a right triangle and the horizontal component, Fx, is the adjacent side:
cos θ = Fx / F
Fx = F · cos θ
Fx = 80 N · cos 35°
Fx = 66 N
Now we can calculate the work (W) done by this force:
W = Fx · x
Where x is the displacement:
W = 66 N · 12 m = 792 J
The work done by the intern is 792 J.
<u>Part B:</u>
Applying the work-energy theorem, the work done is equal to the change in kinetic energy:
W = final kinetic energy - initial kinetic energy
Since the gurney starts from rest, the initial kinetic energy is zero. Then:
W = final kinetic energy
The equation of kinetic energy (KE) is the following:
KE = 1/2 · m · v²
Where:
m = mass of the gurney.
v = velocity.
KE = 792 J
792 J = 1/2 · 42 kg · v²
v²= 2· 792 J / 42 kg
v = 6.1 m/s
The velocity of the gurney when it has moved 12 m is 6.1 m/s.
<u>Part C:</u>
First, let´s find the acceleration of the gurney:
Fx = m · a
Fx/m = a
66N / 42 kg = a
a = 1.6 m/s²
Now using the equation of velocity, let´s find the time at which the gurney has a velocity of 6.1 m/s:
v = v0 + a · t
Where:
v = velocity at time t.
v0 = initial velocity.
a = accleration.
t = time.
v = v0 + a · t
6.1 m/s = 0 + 1.6 m/s² · t
t = 6.1 m/s / 1.6 m/s²
t = 3.8 s
The 12-m journey takes 3.8 s.
Answer:
The displacement is zero miles
Explanation:
The displacement of an object that moves from point A to point B is defined as
Where d is the displacement of the object. The displacement does not depend on the trajectory of the object. It only depends on the linear distance between the end point and the starting point.
In this case we know that the person walks from home to work and then walks from work to home. Therefore, the total displacement is the linear distance between the point where its journey begins and the point where the route ends.
The tour begins on the front porch of your house and ends on the front porch of your house (when you return from work). If we call A to the front porch of the house then the displacement is:
The displacement is zero miles, since the person finishes the journey just where it started (front porch)