Question

At time t=9 seconds, the mass of an object is 51 grams and changing at a rate of 9gs. At this same time, the acceleration is 9ms2 and changing at a rate of â2ms3. By the product rule, the force on the object is changing at the rate of ._________

Answer 1

0.183 N/s

Explanation:

Given

mass of object
`=51 gm`

acceleration
`a\left ( \frac{\mathrm{d} v}{\mathrm{d} t}\right )=9 m/s^2`

`\frac{\mathrm{d} m}{\mathrm{d} t}=9 gm/s`

Force on a object is given by

`F\left ( t\right )=m\left ( t\right )a\left ( t\right )`

Change in force is given by

`\frac{\mathrm{d} F\left ( t\right )}{\mathrm{d} t}=\frac{\mathrm{d} m}{\mathrm{d} t}a\left ( t\right )+m\left ( t\right )\frac{\mathrm{d} a\left ( t\right )}{\mathrm{d} t}`

`\frac{\mathrm{d} F\left ( t\right )}{\mathrm{d} t}=9* 10^(-3)* 9+2* 51* 10^(-3)`

`=183* 10^(-3)=0.183 N/s`