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The distance, x, covered by a particle in time, t, is given as x=a +bc+ct^2 +dt^3
.find the dimension of the constants a, b, c and d​

Respuesta :

mberisso

Answer:

[tex]a[/tex] has units of distance

[tex]b[/tex]  has units of distance over time

[tex]c[/tex]  has units of distance over [tex]time^2[/tex]

[tex]d[/tex] has units of distance over [tex]time^3[/tex]

Explanation:

Since the expression for the distance is:

[tex]x = a+b\,t+c\,t^2+d\,t^3[/tex]

then:

[tex]a[/tex] has units of distance

[tex]b[/tex]  has units of distance over time

[tex]c[/tex]  has units of distance over [tex]time^2[/tex]

[tex]d[/tex] has units of distance over [tex]time^3[/tex]

because we are supposed to be able to add all of the terms and get a distance.  So the products on each term that contains factors of time (t) should be cancelling those time units with units in the denominator of the multiplicative constant s that accompany them.

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