Energy of motion (kinetic energy) Transitional Reasoning Practice

Questions

1. 1.

   An environmental research drone carrying a modular sensor package cruises horizontally at a constant speed of 12 m/s. The sensor package accounts for 75% of the total mass of the combined drone-sensor system. After releasing the sensor package at a drop zone, the drone accelerates so that its kinetic energy equals the original kinetic energy of the combined system before the drop. What is the new cruising speed of the drone?

   • A) 16 m/s
   • B) 24 m/s
   • C) 36 m/s
   • D) 48 m/s
2. 2.

   In a laboratory trial on a frictionless track, cart X with a mass of 4.0 kg moves at a constant speed of 3.0 m/s, while cart Y with a mass of 1.0 kg moves at a constant speed of 8.0 m/s. A third cart, Z, has a mass of 1.0 kg and is launched such that its kinetic energy equals the sum of the kinetic energies of carts X and Y. What is the speed of cart Z?

   • A) 10 m/s
   • B) 11 m/s
   • C) 20 m/s
   • D) 5.5 m/s
3. 3.

   A traffic safety team investigates the relationship between vehicle speed and braking distance on a horizontal test track. When an electric car of mass $m$ travels at an initial speed $v$, its kinetic energy is completely dissipated by a constant braking force $F$, bringing it to rest over a stopping distance $d$. In a second trial under identical road and braking conditions, the car requires a stopping distance of $2.25d$ to come to a complete stop. What is the ratio of the car's initial speed in the second trial to its initial speed in the first trial?

   • A) 1.25
   • B) 2.25
   • C) 5.06
   • D) 1.50
4. 4.

   A robotic transport cart with a mass of 50 kg travels along a straight, horizontal track at a constant initial speed of 4.0 m/s. An onboard motor delivers 1,200 J of net mechanical work to accelerate the cart to a higher cruising speed. Shortly after, a regenerative brake engages and removes 700 J of kinetic energy from the cart. What is the final speed of the cart after braking?

   • A) 2.0 m/s
   • B) 5.0 m/s
   • C) 6.0 m/s
   • D) 8.0 m/s
5. 5.

   A safety engineer monitors an automated guided cart moving along a straight test track at a constant baseline cruising speed. Telemetry data indicates that if the cart increases its speed by 4 m/s while maintaining a constant mass, its kinetic energy increases by 96%. What is the baseline cruising speed of the cart?

   • A) 4 m/s
   • B) 8 m/s
   • C) 10 m/s
   • D) 14 m/s
6. 6.

   An electric delivery van with mass m travels along a straight road at an initial speed of 20 m/s. After cargo is loaded, the total mass of the van increases by 25%, and the driver reduces the cruising speed to 16 m/s. By what percentage does the kinetic energy of the van decrease compared to its initial value?

   • A) It decreases by 20%.
   • B) It decreases by 25%.
   • C) It decreases by 36%.
   • D) It remains unchanged.
7. 7.

   A high-speed train traveling along a straight, horizontal track with an initial speed $v$ engages its braking system to reduce its speed to $\frac{2}{3}v$. Assuming the total mass of the train remains constant, what fraction of the train's initial kinetic energy is dissipated during this braking process?

   • A) $\frac{1}{3}$
   • B) $\frac{4}{9}$
   • C) $\frac{5}{9}$
   • D) $\frac{1}{9}$
8. 8.

   During a laboratory trial on an air track, a sensor measures that a glider of mass $m$ moving at speed $v$ has kinetic energy $K$. A student modifies the setup by attaching weights so that the glider's total mass becomes $3m$, and adjusts the launcher so that the glider acquires a target kinetic energy of $12K$. By what factor must the glider's speed be increased relative to its initial speed $v$ to achieve this target?

   • A) $\sqrt{2}$
   • B) $\sqrt{3}$
   • C) 2
   • D) 4
9. 9.

   A delivery drone moving horizontally along a straight test corridor increases its speed in two successive phases without changing its mass. In the first phase, the drone accelerates from rest to speed $v$, resulting in a change in kinetic energy of $\Delta K_1$. In the second phase, it accelerates from speed $v$ to speed $2v$, resulting in a change in kinetic energy of $\Delta K_2$. What is the ratio $\frac{\Delta K_2}{\Delta K_1}$?

   • A) 3
   • B) 1
   • C) 2
   • D) 4
10. 10.

    In an automated logistics facility, two transport pods move along horizontal test tracks. Pod P has a total mass of $2m$ and travels at a constant speed of $3v$, while Pod Q has a total mass of $6m$ and travels at a constant speed of $v$. An engineer evaluates their motion to design appropriate safety arrestor systems. What is the ratio of the kinetic energy of Pod P to the kinetic energy of Pod Q, $\frac{E_P}{E_Q}$?

    • A) 1
    • B) 1.5
    • C) 3
    • D) 6

Answers and step-by-step solutions appear after you finish the test.