Consider the following set of equations, where s, s0 and r have units of length, t has units of time, v has units of velocity, g and a have units of acceleration. Take k to be dimensionless.Identify if these are dimensionally correct or incorrect.

1)v^2= 2as + kav
2)s = s0 + kat^2
3)a =v^2/r+kv/t
4)t =v/a
5)t = k square root of s/g

1 incorrect

2 correct
3 incorrect
4 correct
5 correct

To determine if the given equations are dimensionally correct or incorrect, we need to check if the units on both sides of each equation match. Let's analyze each equation one by one:

1) v^2 = 2as + kav
The left-hand side has units of (velocity)^2, while the right-hand side has units of (acceleration)(length) + (dimensionless)(acceleration)(velocity). Both sides have the correct units, so this equation is dimensionally correct.

2) s = s0 + kat^2
The left-hand side has units of length, while the right-hand side has units of (length) + (acceleration)(time)^2. Since both sides have the same units, this equation is dimensionally correct.

3) a = v^2/r + kv/t
The left-hand side has units of acceleration, while the right-hand side has units of (velocity)^2/(length) + (dimensionless)(acceleration)/(time). The units do not match, so this equation is dimensionally incorrect.

4) t = v/a
The left-hand side has units of time, and the right-hand side has units of (velocity)/(acceleration). Since both sides have the same units, this equation is dimensionally correct.

5) t = k √(s/g)
The left-hand side has units of time, and the right-hand side has units of dimensionless √(length)/(acceleration). The units do not match, so this equation is dimensionally incorrect.

In summary, equations 1, 2, and 4 are dimensionally correct, while equations 3 and 5 are dimensionally incorrect.