Question

# 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?

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Solution

## Step 1: GivenMass of the truck = $M$Driving force = $F$Let acceleration be ${a}_{1}$After loading mass of truck = $2M$After loading driving force = $\frac{F}{2}$Let acceleration be ${a}_{2}$Step 2: Formula usedWe know that$F=ma$Step 3: Calculating change in accelerationBefore loading$F=M{a}_{1}\phantom{\rule{0ex}{0ex}}{a}_{1}=\frac{F}{M}$After loading $\frac{F}{2}=2M{a}_{2}\phantom{\rule{0ex}{0ex}}{a}_{2}=\frac{F}{4M}$Ratio of accelerations is$\frac{{a}_{1}}{{a}_{2}}=\frac{F}{M}}{F}{4M}}\phantom{\rule{0ex}{0ex}}\frac{{a}_{1}}{{a}_{2}}=4\phantom{\rule{0ex}{0ex}}{a}_{2}=\frac{{a}_{1}}{4}$Hence, acceleration after loading the object becomes $\frac{1}{4}$ the initial acceleration.

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