In this question, one has to carefully understand that the total
number of hours in the day can never be more that 24 hours. based on
this important fact the answer to the question can be very easily
deduced. The only requirement is calculating perfectly.
Number of hours in a day = 24 hours
Percentage of hours of sleep in a day = 33%
Amount of sleep in the day = (33/100) * 24
= 7.92 hours
So 33% of sleep in a day is equal to 7.92 hours. I hope this answer has helped you. In future you can keep the procedure in mind for solving such problems.
Answer:
B
Explanation:
I think this one is correct
Answer:
12 N
Explanation:
Use Newton's second law:
∑F = ma
F = (2.4 kg + 1.3 kg) (3.2 m/s²)
F = 11.84 N
Rounded to two significant figures, the force is 12 N.
The particle has acceleration vector
We're told that it starts off at the origin, so that its position vector at 
is
and that it has an initial velocity of 12 m/s in the positive 
direction, or equivalently its initial velocity vector is
To find the velocity vector for the particle at time 
, we integrate the acceleration vector:
![\vec v=\left[12\,\dfrac{\mathrm m}{\mathrm s}+\displaystyle\int_0^t\left(-2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)\,\mathrm d\tau\right]\,\vec\imath+\left[\displaystyle\int_0^t\left(4.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)\,\mathrm d\tau\right]\,\vec\jmath](https://tex.z-dn.net/?f=%5Cvec%20v%3D%5Cleft%5B12%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%2B%5Cdisplaystyle%5Cint_0%5Et%5Cleft%28-2.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5C%2C%5Cmathrm%20d%5Ctau%5Cright%5D%5C%2C%5Cvec%5Cimath%2B%5Cleft%5B%5Cdisplaystyle%5Cint_0%5Et%5Cleft%284.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29%5C%2C%5Cmathrm%20d%5Ctau%5Cright%5D%5C%2C%5Cvec%5Cjmath)
![\vec v=\left[12\,\dfrac{\mathrm m}{\mathrm s}+\left(-2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\right]\,\vec\imath+\left(4.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\,\vec\jmath](https://tex.z-dn.net/?f=%5Cvec%20v%3D%5Cleft%5B12%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%2B%5Cleft%28-2.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5Cright%5D%5C%2C%5Cvec%5Cimath%2B%5Cleft%284.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5C%2C%5Cvec%5Cjmath)
Then we integrate this to find the position vector at time :
![\vec r=\left[\displaystyle\int_0^t\left(12\,\dfrac{\mathrm m}{\mathrm s}+\left(-2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\right)\,\mathrm d\tau\right]\,\vec\imath+\left[\displaystyle\int_0^t\left(4.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t\,\mathrm d\tau\right]\,\vec\jmath](https://tex.z-dn.net/?f=%5Cvec%20r%3D%5Cleft%5B%5Cdisplaystyle%5Cint_0%5Et%5Cleft%2812%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%2B%5Cleft%28-2.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5Cright%29%5C%2C%5Cmathrm%20d%5Ctau%5Cright%5D%5C%2C%5Cvec%5Cimath%2B%5Cleft%5B%5Cdisplaystyle%5Cint_0%5Et%5Cleft%284.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5C%2C%5Cmathrm%20d%5Ctau%5Cright%5D%5C%2C%5Cvec%5Cjmath)
![\vec r=\left[\left(12\,\dfrac{\mathrm m}{\mathrm s}\right)t+\left(-1.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2\right]\,\vec\imath+\left(2.0\,\dfrac{\mathrm m}{\mathrm s^2}\right)t^2\,\vec\jmath](https://tex.z-dn.net/?f=%5Cvec%20r%3D%5Cleft%5B%5Cleft%2812%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%7D%5Cright%29t%2B%5Cleft%28-1.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2%5Cright%5D%5C%2C%5Cvec%5Cimath%2B%5Cleft%282.0%5C%2C%5Cdfrac%7B%5Cmathrm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2%5C%2C%5Cvec%5Cjmath)
Solve for the time when the 
coordinate is 18 m:
At this point, the coordinate is
so the answer is C.
