The acceleration a of an object is given by the equation a=a+bt+ct^3 where t refers to time. (a) what are the dimensions of a, b, and c? (b) what are the si units for the constants a, b, and c?

(a) A =

B =

(b) A =

B =

C =

Solution:

The acceleration of a body is the rate at which the velocity of the body changes.

Thus

The SI unit of velocity of an object is and its dimension is [LT^{- 1}] and for time, T the SI unit is second, s and dimension is [T] and hence

The SI unit and dimension for the acceleration of an object is and [LT^{- 2}] respectively.

Now, as per the question:

acceleration, a =

(a) Now, according to the homogeneity principle in dimension, the dimensions on both the sides of the eqn must be equal,

For the above eqn:

Thus the dimensions of :

A =

BT =  

Thus for B

B =

(b) For the units of A, B and C, we will make use of their respective dimensional formula from part (a)

where

L corresponds to length in meter(m)

T corresponds to time in seconds(s)

Now, for:

A =

B =

C =

step-by-step explanation:

we are given

we have to simplify it

firstly, we will factor it

now, we can cancel like terms

now, we can combine it

so, we get

since you're a real machine, your ama is always less than your ima, because you can never totally eliminate friction.