A bike rider rides at an average of 12 m/s for 30 minutes. How many km can the rider travel in that time? Show your work.
1 answer:
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Given that,
Mass of object = 9.90 kg
Time =5.40 s
Suppose the force is (2.00i + 9.00j + 5.30k) N, initial position is (2.70i - 2.90j + 5.50k) m and final position is (-4.10i + 3.30j + 5.40k) m.
We need to calculate the displacement
Using formula of displacement
Where, = initial position
= final position
Put the value into the formula
(a). We need to calculate the work done on the object
Using formula of work done
Put the value into the formula
(b). We need to calculate the average power due to the force during that interval
Using formula of power
Where, P = power
W = work
t = time
Put the value into the formula
(c). We need to calculate the angle between vectors
Using formula of angle
Put the value into the formula
Hence, (a). The work done on the object by the force in the 5.40 s interval is 41.67 J.
(b). The average power due to the force during that interval is 7.71 Watt.
(c). The angle between vectors is 79.7°
To solve this problem we will use the kinematic equations of angular motion, starting from the definition of angular velocity in terms of frequency, to verify the angular displacement and its respective derivative, let's start:
The angular displacement is given as the form:
In the equlibrium we have to and in the given position we have to
Derived the expression we will have the equivalent to angular velocity
Replacing,
Finally
Therefore the maximum angular displacement is 9.848°