Question

If kinetic energy K depends on velocity v, acceleration a and density p of an object, find the expression for K

Answer 1

K = kpv⁸/a³ is the expression for K, where, kinetic energy K depends on velocity v, acceleration a and density p of an object.

Kinetic energy is the energy of an object that it possesses due to its motion.

From given, we have, kinetic energy K depends on velocity v, acceleration a and density p of an object.

The expression for the kinetic energy K is given by as follows:

$Here, K \propto \vap K = k v^a a^b p^c---(1)$

$[ML^2T ^{-2}] = k [LT^{-1}]^a × [LT^{-2}]^b × [ML^{-3}]^c [ML^2T^{-2}]$

$= k [L^{a+b-3c} M^c T^{-a -2b}]$

$Now, c = 1 b = -3 a = 8$

$From (1) \\\\K = k v^8 a^{-3} p^1$

$\therefore K = k \dfrac { pv^8}{a^3}$

Answer 2

Answer:

Please refer to the attachment.

Hope this helped.

@Shailene