Question

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 15/ms2. If the same force acts upon another object whose mass is

10kg, what is this object's acceleration?

Answer 1

`a = 6m/s^2`

Explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

`a\ \alpha\ (1)/(m)`

Convert variation to equality

`a = (F)/(m)`; Where F is the constant of variation (Force)

Make F the subject of formula;

`F = ma`

When mass = 4kg; Acceleration = 15m/s²

`F = 4 * 15`

`F = 60N`

When mass = 10kg; Substitute 60 for Force

`F = ma`

`60 = 10 * a`

`60 = 10a`

Divide both sides by 10

`(60)/(10) = (10a)/(10)`

`a = 6m/s^2`

Hence, the acceleration is
`a = 6m/s^2`