Question

Which of the following quantities have the dimensions of an acceleration? Which of the following quantities have the dimensions of an acceleration?

a. v²/x
b. xt²
c. x/t²
d. v/t

Answer 1

a)
`(v^2)/(x)`

c)
`(x)/(t^2)`

d)
`(v)/(t)`

Step-by-step explanation:

Acceleration :

Acceleration is the rate of change of velocity of the particle.

The unit of acceleration is m/s².

In mathematical form,

`a=(dv)/(dt)`

We will check the all option on base of unit

(a).
`(v^2)/(x)`

Where, v = velocity

x = position

The unit of velocity and position are m/s and m.

The dimension formula of velocity and position

`v = LT^(-1)`

`x=L`

Put the unit in the given equations

`(v^2)/(x)=(L^2T^(-2))/(L) =(L)/(T^2)`

(b).
`xt^2=L* T^2`

(c).
`(x)/(t^2)=(L)/(T^2)`

(d).
`(v)/(t)=(LT^(-1))/(T)=(L)/(T^2)`

Hence, This is the required solution.

Answer 2

Step-by-step explanation:

The acceleration of an object is given by :

`a=(v-u)/(t)`

Dimension of velocity is,
`[v]=[LT^(-1)]`

Dimension of time is,
`[t]=[T]`

Dimension of acceleration is,
`[a]=[LT^(-2)]`

Option 1.

`(v^2)/(x)=[LT^(-2)]`

Option 2.

`xt^2=[LT^2]`

Option 3.

`(x)/(t^2)=[LT^(-2)]`

Option 4.

`(v)/(t)=[LT^(-2)]`

So, from above calculations, it is clear that option (1),(3) and (4) have the dimensions of acceleration. Hence, this is the required solution.