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.
(d) Acceleration is a vector quantity
Answer:
Explanation:
No of atoms of Ra in 1 g of sample = 6.023 x 10²³ / 226
N = 2.66 x 10²¹
disintegration constant λ = .693 / half life
half life = 1620 x 365 x 60 x 60 x 24 = 5.1 x 10¹⁰ s
disintegration constant λ = .693 / 5.1 x 10¹⁰
radioactivity dn / dt = λN
= (.693 / 5.1 x 10¹⁰ ) x 2.66 x 10²¹
= .3614 x 10¹¹ per sec
= 3.614 x 10¹⁰ / s
The answer for this would be A. since power is Joules/seconds and energy is rated in Joules