KEY2PHYSICS

#PROBLEM-60038

Suppose quantity $s$ is a length and quantity $t$ is a time. Suppose the quantities $v$ and $a$ are defined by $v=ds/dt$ and $a=dv/dt$ . What is the dimension of $v$ ?

$[v]=L^2T^{2}$

$[v]=LT^{-1}$

$[v]=L^{-2}T^{-1}$

$[v]=LT$

#PROBLEM-60039

What is the dimension of the quantity $a$ ?

$[a]=LT^{-2}$

$[a]=L^{-1}T^{-2}$

$[a]=LT^{2}$

$[a]=L^{-1}T$

#PROBLEM-60040

What are the dimensions of $\int v\; dt$ ?

$\big[\int v\;dt \big]=LT^{-2}$

$\big[\int v\;dt \big]=L^{-1}$

$\big[\int v\;dt \big]=LT$

$\big[\int v\;dt \big]=L$

#PROBLEM-60041

What are the dimensions of $\int a\; dt$ ?

$\big[ \int a\: dt\big]=L^2T$

$\big[ \int a\: dt\big]=LT^{-1}$

$\big[ \int a\: dt\big]=L^{-2}T^{-1}$

$\big[ \int a\: dt\big]=LT^{-2}$

#PROBLEM-60042

What are the dimensions of $\frac{da}{dt}$ ?

$\big[\frac{da}{dt}\big]=LT$

$\big[\frac{da}{dt}\big]=LT^{-3}$

$\big[\frac{da}{dt}\big]=L^{-1}T^{-3}$

$\big[\frac{da}{dt}\big]=L^{-3}T$