Question

if force F and velocity v is related to time t & mass m, acceleration a according to the equation

F/a=t^x m^y 

then the value of x=

Answer 1

The units of accelration are:

$$[a] = m/s^2$$

of force:

$$[F] = kg\cdot m/s^2$$

of time $[t] = s$ and mass $[m] = kg$. Thus, obtain:

$$\dfrac{[F]}{[a]} = [t]^x[m]^y\\ \dfrac{kg\cdot m\cdot s^2}{s^2\cdot m} = kg^x\cdot s^y\\ kg = kg^x\cdot s^y$$

Comparing the sides of the las equation, obtain:

$$x = 1, y = 0$$

Answer. $x = 1, y = 0.$