Question

In the following equations, the distance x is in meters, the time tin seconds. and the velocity v is in meters per second. whatare the SI units of the constants c1 andc2?

(A) x = c1 +c2t
(B) x = .5c1t^2
(C) v^2 = 2c1x
(D) x = c1cosc2t
(E) v^2 =2c1v-(c2x)^2

Answer 1

Step-by-step explanation:

Given that,

The distance x is in meters.

The time t is in seconds.

The velocity v is in meter/ second.

We need to calculate the SI units the constants c₁ and c₂

(A).
`x =c_(1)+c_(2)t`

Put the unit in to the equation

`m= m+m/s* s`

Here,
`c_(1)=m`

`c_(2)=m/s`

So,

`m = m`

(B).
`x=0.5c_(1)t^2`

Put the unit in to the equation

`m=0.5* m/s^2* s^2`

Here,
`c_(1)=m/s^2`

So,
`m=0.5 m`

(C).
`v^2=2c_(1)x`

Put the unit in to the equation

`m^2/s^2=2* m/s^2* m`

Here,
`c_(1)=m/s^2`

So,
`m^2/s^2=2m^2/s^2`

(D).
`x=c_(1)\cos c_(2)t`

Put the unit in to the equation

`m=m*\cos((1)/(s)* s)`

Here,
`c_(1) =m`

`c_(2)=(1)/(s)`

`\cos(c_(2)t)` =dimension less

So,
`m=m`

(E).
`v^2=2c_(1)v-(c_(2)x)^2`

Put the unit in to the equation

`m^2/s^2=2* m/s* m/s-((1)/(s^2)* m^2)`

Here,
`c_(1)=m/s`

`c_(2)=(1)/(s)`

So,
`m^2/s^2=m^2/s^2`

Hence, This is the required solution.

Answer 2

A) c₁ = m, c₂ = m/s

B) c₁ = m/s²

C) c₁ = m/s²

D) c₁ = m/s c₂ = °

E) c₁ = m/s , c₂ = /s

Step-by-step explanation:

A) x = c₁ + c₂t

⇒m = m + (m/s)s (Only same units can be added)

⇒m = m

So, c₁ = m, c₂ = m/s

B) x = 0.5c₁t²

⇒m = 0.5 (m/s²)s²

⇒m = m

So, c₁ = m/s²

C) v² = 2c₁x

⇒m²/s² = 2 (m/s²)m

⇒m²/s² = m²/s²

So, c₁ = m/s²

D) x = c₁ cos(c₂)t

⇒m = (m/s) cos(°)s

⇒m = m

So, c₁ = m/s c₂ = °

E) v² = 2c₁v-(c₂x)²

⇒m²/s² = 2(m/s)(m/s)-(1/s²)(m²)

⇒m²/s² =m²/s²

So, c₁ = m/s , c₂ = /s