Question

lets continue to practice. complete these without using your notes or peers.

characteristic	dimension	si unit	equation
mass	m	kg	-
time	t	s	-
area		m²	example: a = lw
volume		l or m³
velocity		m/s
acceleration		m/s²
force		n
work		j
power		w
pressure		pa

Explanation:

Step1: Recall dimension - area

Area is the product of two lengths, so its dimension is $L^2$.

Step2: Recall dimension - volume

Volume is the product of three lengths, so its dimension is $L^3$.

Step3: Recall dimension - velocity

Velocity is distance (length) per time, so its dimension is $L/T$.

Step4: Recall dimension - acceleration

Acceleration is change in velocity per time, so its dimension is $L/T^2$.

Step5: Recall dimension - force

Force is mass times acceleration ($F = ma$), so its dimension is $M\times L/T^2=ML/T^2$.

Step6: Recall dimension - work

Work is force times distance ($W = Fd$), so its dimension is $ML/T^2\times L = ML^2/T^2$.

Step7: Recall dimension - power

Power is work per time ($P=W/t$), so its dimension is $ML^2/T^2\div T=ML^2/T^3$.

Step8: Recall dimension - pressure

Pressure is force per area ($P = F/A$), so its dimension is $ML/T^2\div L^2 = M/LT^2$.

Step9: Recall equations

Area of rectangle: $A = LW$; Volume of cube: $V = L^3$; Velocity: $v=\frac{d}{t}$; Acceleration: $a=\frac{\Delta v}{\Delta t}$; Force: $F = ma$; Work: $W = Fd$; Power: $P=\frac{W}{t}$; Pressure: $P=\frac{F}{A}$

Answer:

Characteristic	Dimension	SI Unit	Equation
Mass	M	kg	-
Time	T	s	-
Area	$L^2$	$m^2$	$A = LW$ (for rectangle)
Volume	$L^3$	$m^3$ or L	$V = L^3$ (for cube)
Velocity	$L/T$	m/s	$v=\frac{d}{t}$
Acceleration	$L/T^2$	$m/s^2$	$a=\frac{\Delta v}{\Delta t}$
Force	$ML/T^2$	N	$F = ma$
Work	$ML^2/T^2$	J	$W = Fd$
Power	$ML^2/T^3$	W	$P=\frac{W}{t}$
Pressure	$M/LT^2$	Pa	$P=\frac{F}{A}$