Question

a fuel truck has an initial mass of b kg and an initial acceleration of 3x m/s². after delivering the fuel to gas stations, the trucks mass is now 0.15 times its initial mass. if the trucks acceleration increases by x times, which expression represents the force of the truck after deliveries? 0.15x 0.45bx² 3bx 0.45bx

Explanation:

Step1: Determine the final mass

The initial mass is $b$ kg and the final mass is 0.15 times the initial mass, so the final mass $m = 0.15b$ kg.

Step2: Determine the final acceleration

The initial acceleration is $3x$ m/s² and it increases by $x$ times. So the final acceleration $a=3x\times x = 3x^{2}$ m/s².

Step3: Calculate the force

According to Newton's second - law $F = ma$. Substitute $m = 0.15b$ and $a = 3x^{2}$ into the formula. Then $F=0.15b\times3x^{2}=0.45bx^{2}$ N.

Answer:

$0.45bx^{2}$