Energy of motion (kinetic energy) Transitional Reasoning Download PDF

Questions

1. 1.

   In an automated distribution center, two identical logistics carts, each with a mass of 400 kg, travel along the same straight horizontal aisle. Cart 1 moves east at a constant speed of 3.0 m/s, while Cart 2 moves west at a constant speed of 4.0 m/s. What is the total kinetic energy of this two-cart system?

   • A) 400 J
   • B) 1400 J
   • C) 5000 J
   • D) 10,000 J
2. 2.

   A robotic rail transporter consists of a 250 kg drive engine coupled to a 750 kg cargo wagon, traveling together along a straight horizontal track at a constant speed of 15 m/s. During transit, the cargo wagon is decoupled and safely brought to rest, while the drive engine accelerates forward. If the final kinetic energy of the drive engine alone equals the initial total kinetic energy of the combined transporter system, what is the final speed of the drive engine?

   • A) 30 m/s
   • B) 60 m/s
   • C) 45 m/s
   • D) 15 m/s
3. 3.

   An aerospace engineering team analyzes the impact hazards of orbital space debris and micrometeorites. A spherical micrometeorite with radius $r$ and mass $m$ travels at speed $v$, possessing a kinetic energy of $K$. A second spherical micrometeorite composed of the same uniform material has a radius of $2r$ and moves at a speed of $v/2$. What is the kinetic energy of the second micrometeorite in terms of $K$?

   • A) $0.5K$
   • B) $K$
   • C) $4K$
   • D) $2K$
4. 4.

   During a performance evaluation on a straight, frictionless test track, telemetry records the kinetic energy of an automated inspection vehicle as its speed increases by $5\text{ m/s}$. The data indicates that during this acceleration phase, the vehicle's kinetic energy rises from $80\text{ J}$ to $180\text{ J}$. What was the vehicle's initial speed before this speed increase?

   • A) 4 m/s
   • B) 10 m/s
   • C) 15 m/s
   • D) 20 m/s
5. 5.

   A traffic safety team evaluates the emergency stopping performance of an electric cart on a level track where brakes deliver a constant retarding force until the cart stops. At an initial speed of 12 m/s, the cart possesses a kinetic energy of 28.8 kJ and comes to rest over a braking distance of 16 m. If the cart instead begins braking from a speed of 18 m/s under the same retarding force, what total braking distance is required to dissipate its kinetic energy?

   • A) 24 m
   • B) 36 m
   • C) 48 m
   • D) 64 m
6. 6.

   During a handling test on a flat proving ground, a telemetry system records the velocity of a 500 kg prototype vehicle. The vehicle initially travels due north at a constant speed of 12 m/s and later travels due east at a constant speed of 16 m/s. What is the change in the vehicle's kinetic energy between these two states?

   • A) 4 kJ
   • B) 28 kJ
   • C) 56 kJ
   • D) 100 kJ
7. 7.

   A safety engineer tests an automated transport cart operating along a horizontal path. When the empty cart of mass $M$ travels at speed $v$, its kinetic energy is $K$. During a delivery, cargo is added so that the cart's total mass increases by $25\%$, while safety regulations require its travel speed to decrease by $20\%$. What is the kinetic energy of the loaded cart in terms of $K$?

   • A) $0.80 K$
   • B) $1.00 K$
   • C) $1.25 K$
   • D) $0.64 K$
8. 8.

   During a performance test of a prototype electric vehicle on a straight horizontal track, engineers evaluate how kinetic energy accumulates over successive acceleration stages. In Stage 1, the vehicle accelerates from rest to a speed $v$, gaining a kinetic energy of $E$. In Stage 2, the vehicle continues accelerating from speed $v$ to a final speed of $3v$. How much additional kinetic energy does the vehicle gain during Stage 2 in terms of $E$?

   • A) $8E$, because the increase in kinetic energy depends on $(3v)^2 - v^2 = 8v^2$.
   • B) $4E$, because the speed increases by $2v$ and kinetic energy is proportional to the square of that change, $(2v)^2$.
   • C) $9E$, because the kinetic energy at the final speed of $3v$ is nine times the energy at speed $v$.
   • D) $2E$, because the speed increase of $2v$ in Stage 2 is double the speed increase of $v$ in Stage 1.
9. 9.

   In an automated logistics facility, sensor data tracks test parcels moving along a frictionless horizontal track. Parcel X has a mass of $m$ and travels at speed $v$, resulting in a kinetic energy of $E$. A technician needs Parcel Y, which has a mass of $1.5m$, to operate with a kinetic energy of $6E$. What speed must Parcel Y have in terms of $v$?

   • A) $0.5v$
   • B) $1.5v$
   • C) $2.0v$
   • D) $4.0v$
10. 10.

    In a mechanics laboratory, two remote-controlled test carts, Cart P and Cart Q, move across a frictionless horizontal surface. Cart P has a mass of $m$ and moves at a constant speed of $2v$, while Cart Q has a mass of $3m$ and moves at a constant speed of $v$. Which statement correctly compares the kinetic energy of Cart P to Cart Q and provides the correct physical justification?

    • A) Cart P has $\frac{4}{3}$ times the kinetic energy of Cart Q because kinetic energy depends on the square of speed, which outweighs the larger mass of Cart Q.
    • B) Cart Q has $\frac{3}{2}$ times the kinetic energy of Cart P because mass contributes more heavily to translational kinetic energy than velocity.
    • C) Cart P and Cart Q have identical kinetic energies because the doubled velocity of Cart P is balanced by the greater mass of Cart Q.
    • D) Cart P has $2$ times the kinetic energy of Cart Q because kinetic energy scales in direct linear proportion to both mass and speed.