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A truck of mass $M$ is moved under a force $F$. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?
As given, the mass of the truck $=M$
Force applied $=F$
Then acceleration $a=\frac{F}{M}$ ........ $(i)$
If the truck is loaded with an object having a mass equal to the truck, then mass $=2M$
And the force is halved, so it becomes $\frac{F}{2}$
So, acceleration $a'=\frac{\frac{F}{2}}{2M}$
$=\frac{F}{4M}$
$=\frac{1}{4}\times \frac{F}{M}$
$=\frac{1}{4}\times a$ [from $(i)\ a=\frac{F}{M}$]
So, acceleration $a'=\frac{a}{4}$
Therefore, If the truck is loaded with an object equal to the mass of the truck and the driving force is halved, then the acceleration becomes one forth.
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