Checkpoint: Solving Variation Problems Solution

In physics, force is the product of mass and acceleration, $F = m a .$ If the mass of an object is 542 kilograms when accelerating at $13 {\frac{m}{s}}^{2},$ what is the acceleration of the same object with a force of 5230.3 Newtons?

$F = m a F = 542 (13) F = 7046 F = m a 5230.3 = 542 a a = 9.65$

Check:

$\begin{array}{rcl} \frac{F}{a} : \frac{7046}{13} & = & \frac{5230.3}{9.65} ✓ \end{array}$

Note

You do not need to calculate the original force. Only the mass and the final force of the object are needed to determine the final acceleration. Since the mass remains the same, you can write the ratio in terms of m to check. 

Q: What is the value of the constant of variation for this problem?

A: 542 kg 

Because the mass remains the same, it is the constant of variation in this problem.