Answer:
a) 600 meters
b) between 0 and 10 seconds, and between 30 and 40 seconds.
c) the average of the magnitude of the velocity function is 15 m/s
Explanation:
a) In order to find the magnitude of the car's displacement in 40 seconds,we need to find the area under the curve (integral of the depicted velocity function) between 0 and 40 seconds. Since the area is that of a trapezoid, we can calculate it directly from geometry:
![Area \,\,Trapezoid=(\left[B+b]\,(H/2)\\displacement= \left[(40-0)+(30-10)\right] \,(20/2)=600\,\,m](https://tex.z-dn.net/?f=Area%20%5C%2C%5C%2CTrapezoid%3D%28%5Cleft%5BB%2Bb%5D%5C%2C%28H%2F2%29%5C%5Cdisplacement%3D%20%5Cleft%5B%2840-0%29%2B%2830-10%29%5Cright%5D%20%5C%2C%2820%2F2%29%3D600%5C%2C%5C%2Cm)
b) The car is accelerating when the velocity is changing, so we see that the velocity is changing (increasing) between 0 and 10 seconds, and we also see the velocity decreasing between 30 and 40 seconds.
Notice that between 10 and 30 seconds the velocity is constant (doesn't change) of magnitude 20 m/s, so in this section of the trip there is NO acceleration.
c) To calculate the average of a function that is changing over time, we do it through calculus, using the formula for average of a function:
Notice that the limits of integration for our case are 0 and 40 seconds, and that we have already calculated the area under the velocity function (the integral) in step a), so the average velocity becomes:
Answer:
0.72
Explanation:
= Time period of oscillation = 1.5 s
Angular frequency is given as
= Amplitude of oscillation = 40 cm = 0.40 m
= Coefficient of static friction = ?
= acceleration of the block
= mass of the block
Maximum acceleration of the block is given as
frictional force is given as
As per newton's second law
If the box is a distance 1.81 m from the rear of the truck when the truck starts,<span> ... Force of Friction = mu_s * Normal Force( </span>M<span> * G) ... The </span>box starts<span> moving! ... Now that the </span>box<span> is moving, the bed of the </span>truck<span> pulls at it with 17.4 ... out how </span>long<span> it will take the </span>box<span> to reach the back of the </span>truck<span>. ... T^2 = 2 * </span>1.81<span> / .64</span>
Kinetic energy is proportional to the square of the speed. So when anything or anybody speeds up, its kinetic energy increases.
The change in momentum of the car is 45,000 kg m/s
Explanation:
The change in momentum of an object is given by:
where
m is the mass of the object
u is its initial velocity
v is its final velocity
For the car in this problem, we have
m = 900 kg
u = 30 m/s
v = 80 m/s
Therefore, the change in momentum is:
Learn more about momentum:
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