Explanation:
It is given that, the position of a particle as as function of time t is given by :

Let v is the velocity of the particle. Velocity of an object is given by :

![v=\dfrac{d[(8t+9)i+(2t^2-8)j+6tk]}{dt}](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7Bd%5B%288t%2B9%29i%2B%282t%5E2-8%29j%2B6tk%5D%7D%7Bdt%7D)

So, the above equation is the velocity vector.
Let a is the acceleration of the particle. Acceleration of an object is given by :

![a=\dfrac{d[8i+4tj+6k]}{dt}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7Bd%5B8i%2B4tj%2B6k%5D%7D%7Bdt%7D)

At t = 0, 

Hence, this is the required solution.
Answer:
v = 0.489 m/s
Explanation:
It is given that,
Mass of a box, m = 1.5 kg
The compression in the spring, x = 6.5 cm = 0.065 m
Let the spring constant of the spring is 85 N/m
We need to find the velocity of the box (v) when it hit the spring. It is based on the conservation of energy. The kinetic energy of spring before collision is equal to the spring energy after compression i.e.


So, the speed of the box is 0.489 m/s.
Similar elements with similar properties were in the same groups and periods for instance lithium(Li) and sodium(Na) are alkaline metals and so belong to the same group (that is group 1).Also Hydrogen(H) and Helium(He) both have only one shell or energy level and so belong to the same period.
It depends on what that "certain amount" is.
Answer:
volumme =0.36 ml
Explanation:
total heat required can be obtained by using following formula
.......(1)
where,
m - mass of water,
C - specific heat capacity of water and = 4.184 j g^{-1} °C
- total change in temperature. = 10°C
The density of water is 1 g/cc. hence, 200 mL of water is equal to 200 g
putting all value in the above equation (1)
q = 200*4.184* 10 ° = 8368 J.
Therefore total number of moles of ethanol required to supply 8368 J of heat is
The molar mass of ethanol is 46 g/mol.
The mass of ethanol required is 46* 0.006117 = 0.28138 g
The density of ethanol is 0.78 g/ml.
The volume of ethanol required is
