1)v^2= 2as + kav
m²/s²=(m/s²)•m +(m/s²)•(m/s)
=> incorrect
2)s = s0 + kat^2
m= m + (m/s²)•s²=> correct
….
3 incorrect
4 correct
5 correct
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
m²/s²=(m/s²)•m +(m/s²)•(m/s)
=> incorrect
2)s = s0 + kat^2
m= m + (m/s²)•s²=> correct
….
3 incorrect
4 correct
5 correct
1) Equation: v^2 = 2as + kav
The left-hand side of the equation has units of (velocity)^2, while the right-hand side has units of (acceleration)(length) + (dimensionless)(acceleration)(velocity). Since both sides of the equation have the same units, this equation is dimensionally correct.
2) Equation: s = s0 + kat^2
The left-hand side has units of length, while the right-hand side has units of (length) + (acceleration)(time^2). These units do not match, so this equation is dimensionally incorrect.
3) Equation: a = v^2/r + kv/t
The left-hand side has units of acceleration, while the first term on the right-hand side has units of (velocity)^2/(length) and the second term has units of (dimensionless)(acceleration)(1/time). Since the units do not match, this equation is dimensionally incorrect.
4) Equation: t = v/a
Both sides of the equation have units of time, so this equation is dimensionally correct.
5) Equation: t = k√(s/g)
The left-hand side has units of time, while the right-hand side has units of (dimensionless) times the square root of (length)/(acceleration). Since the units do not match, this equation is dimensionally incorrect.
In summary, equations 1 and 4 are dimensionally correct, while equations 2, 3, and 5 are dimensionally incorrect.