Question

The position of a particle along the x-axis depends on the time according to the equation according to the
at2−bT3
, where x is in metres and t in seconds. What are the dimensions of and units of a and b?
a. LT−2
,
m=s2
;
LT−3
,
m=s3

b. LT2
,
m=s−2
;
LT3
,
m=s−3

c. L−1T−2
,
m−1=s2
;
LT−3
,
m=s3

d. LT−2
,
m=s2
;
L−2T−3
,
m−2=s3

Answer 1

Answer on Question#41348, Physics, Mechanics

The position of a particle along the x-axis depends on the time according to the equation according to the at²-bt³, where x is in metres and t in seconds. What are the dimensions of and units of a and b?

a. LT⁻², m/s²; LT⁻³, m/s³

b. LT², m/s⁻²; LT³, m/s⁻³

c. L⁻¹T⁻², m⁻¹/s²; LT⁻³, m/s³

d. LT⁻², m/s²; L⁻²T⁻³, m⁻²/s³

Solution:

Given:

$$x = a t ^ {2} - b t ^ {3}$$

In this equation x is a distance. The unit of x is length (L) in meters (m).

So both terms being subtracted, at² and bt³, have the units of length.

Since at² has units of L, since you get L by multiplying a by a time squared (T²), then a must have units of L/T² or m/s² (LT⁻²).

We can do similar reasoning for bt³. We get L out by multiplying b by a time cubed. So b has to have units of L divided by time³.

Thus b dimension is LT⁻³, m/s³.

Answer. a. LT⁻², m/s²; LT⁻³, m/s³.

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