Due to budget cuts, a city no longer hires mechanics to fix fire engines. While enroute to rescue a cat from a tree, a 16,000 kg fire engine accelerates from a rest at a stop sign at 1 m/s2 when the pump, fire hoses, and various other implements of destruction (total mass of 4000 kg) fall off.
a. What is the acceleration AFTER THE EQUIPMENT FALLS OFF?
b. What is the velocity 3 seconds AFTER THE EQUIPMENT FALLS OFF?
c. What is the kinetic energy of the truck AFTER THE EQUIPMENT FALLS OFF?
Find the mass after the equipment falls off and use the force which remains the same to find the required acceleration. Use the equation of kinematics to find the required velocity after the given time as shown below
$$ \begin{array}{l} \text { a) Initially fora } F=\text { Ma } \\ =(16000 \text { icg })\left(1 \mathrm{~m} / \mathrm{s}^{2}\right) \\ \text { = } 16000 \mathrm{~N} \\ \text { Now, when equipment falls off, mass is, } \\ \qquad M^{\prime}=16000 \mathrm{~kg}-4000 \mathrm{~kg}=12000 \mathrm{kg} \\ \text { force remains same, } \\ \text { So, } a^{\prime}=\frac{F}{M^{\prime}}=\frac{16000 \mathrm{~N}}{120001 \mathrm{~g}}=1.33 \mathrm{~m} / \mathrm{s}^{2} \\ \end{array} $$
\(\begin{aligned} \text { b) } v_{f} &=v_{i}+a^{\prime} t \\ &=0+\left(1 \cdot 33 \mathrm{~m} / \mathrm{s}^{2}\right)(3 \mathrm{~s})=4 \mathrm{~m} / \mathrm{s} \end{aligned}\)
c) \(\quad K E=\frac{1}{2} M^{\prime} v_{f}^{2}=\frac{1}{2}(12000 \mathrm{~kg})(4 \mathrm{~m} / \mathrm{s})^{2}=96000 \mathrm{~J}\)
Due to budget cuts, a city no longer hires mechanics to fix fire engines. While enroute to rescue a cat from a tree, a 16,000 kg fire engine accelerates from a rest at a stop sign at 1 m/s2 when the pump, fire hoses, and various other implements of destru