Suppose quantity s is a length and quantity t is a time. suppose the quantities v and a are defined by v = ds/dt and a = dv/dt. (a) what is the dimension of v? (b) what is the dimension of the quantity a? what are the dimensions of (c) ∫vdt,(d) ∫adt, and (e) da/dt?

a)

b)

c)

d)

e)

Step-by-step explanation:

Let define some notation:

[L]= represent longitude , [T] =represent time

And we have defined:

s(t) a position function

Part a

If we do the dimensional analysis for v we got:

Part b

For the acceleration we can use the result obtained from part a and we got:

Part c

From definition if we do the integral of the velocity respect to t we got the position:

And the dimensional analysis for the position is:

Part d

The integral for the acceleration respect to the time is the velocity:

And the dimensional analysis for the position is:

Part e

If we take the derivate respect to the acceleration and we want to find the dimensional analysis for this case we got:

what is the graph

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: