Question

Inverse variation?
When a constant force acts upon an object, the acceleration of the object varies inversely with it’s mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 14m/s^2. If the same force upon another object whose mass is 7kg. What is this objects acceleration?

Answer 1

Answer:

An Inverse variation states that a relationship between two variables in which the product is always constant.

If one of the variable increases then the other decreases in proportion so that the product is unchanged.

if y is inversely proportional to x, then the equation is of the form

$y = \frac{k}{x}$ , where k is constant.

As per the given condition, A constant force acts upon an object, the acceleration of the object varies inversely with it's mass.

i.e, $a \propto \frac{1}{m}$

By definition of inverse variation;

$a = \frac{F}{m}$ . ......[1]  ,where F is the constant force.

It is given that an object has mass(m)= 4kg and the acceleration of an object(a) = 14 $m/s^2$

Substitute these in [1] to find the constant force F;

$14 = \frac{F}{4}$

or

$F =14 \times 4 = 56 kg m/s^2$

Now, if the same force acts upon the another object whose mass (m) = 7 kg then calculate acceleration.

[1]⇒  $a = \frac{56}{7} = 8 m/s^2$

therefore, the acceleration of an another object is, $8 m/s^2$