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Topic 3.1: Practice Sheet — Translational Kinetic Energy

Name: _______________________________ Date: _______________ Period: ______

Directions: For every calculation, write $K=\tfrac12mv^2$ first, identify the correct speed (never a negative sign — speed is always the magnitude), then substitute numbers. Show every step.

  1. A 2.0 kg object moves at 3.0 m/s. Find its kinetic energy.
  2. A ball is thrown straight up. At the exact peak of its path, is the ball's kinetic energy positive, negative, or zero? Explain.
  3. A 0.20 kg object starts from rest and reaches a speed of 5.0 m/s. Find its final kinetic energy and its change in kinetic energy since it started from rest.
  4. The position of a 5 kg object moving in one dimension changes from $x=8\text{ m}$ at $t=4\text{ s}$ to $x=0\text{ m}$ at $t=5\text{ s}$. Find the object's kinetic energy at $t=5\text{ s}$.
  5. A projectile moves vertically upward with acceleration directed downward (gravity). Is the projectile's kinetic energy increasing, decreasing, or constant while it rises? Explain using the relationship between kinetic energy and speed.

Reference Frames

  1. A car of mass 1300 kg travels on a highway at 25 m/s relative to the road. It passes a truck moving in the same direction at 15 m/s relative to the road. a) Find the car's kinetic energy relative to the road. b) Find the car's kinetic energy relative to an observer riding in the truck. c) Explain, in words, why these two answers are different even though they describe the same car at the same instant.

Reading a Graph

  1. A velocity-time graph shows an object of mass 0.20 kg with velocity increasing linearly from $0$ to $5\text{ m/s}$ over the first 2 seconds, then remaining constant at $5\text{ m/s}$ for the next 3 seconds. a) Find the object's change in kinetic energy over the full 5 seconds. b) Is the object's kinetic energy changing at all during the last 3 seconds? Explain.

AP Classroom-Style Questions

(Modeled directly on the real Topic 3.1 AP Classroom quiz question styles — reference-frame reasoning, graph reading, and non-negativity traps.)

  1. At time $t_1$, a car travels west with speed $v$. At time $t_2$, the same car travels east with speed $v$ (same speed, opposite direction). Which of the following correctly describes the change in kinetic energy $\Delta K$ of the car between $t_1$ and $t_2$? (A) $\Delta K = 0$, because the mass and speed of the car are the same at both times (B) $\Delta K = 0$, because the car's kinetic energy is negative at $t_1$ and positive at $t_2$, which cancels (C) $\Delta K > 0$, because the car's velocity changed direction (D) $\Delta K > 0$, because kinetic energy is always increasing over time
  2. Two carts, A and B, have the same mass. At a certain instant, Cart A moves right at speed $v$ relative to the ground, and Cart B moves left at speed $v$ relative to the ground. Find the kinetic energy of Cart A relative to Cart B, and compare it to the kinetic energy of Cart A relative to the ground. Which is larger, and by what factor?
  3. A 0.20 kg object travels along a straight track. A graph of its speed versus time shows the speed decreasing linearly from $8\text{ m/s}$ at $t=0$ to $3\text{ m/s}$ at $t=2\text{ s}$. Find the object's change in kinetic energy over this interval, and state whether the change is positive or negative before calculating — explain how you know the sign in advance.
  4. A student claims: "If an object's kinetic energy is the same at two different times, then its velocity must also be the same at both times." Evaluate this claim. Is it true, false, or true only under certain conditions? Justify your answer using the relationship between $K$ and $v$.

Keep this sheet — it's part of your semester study materials, same as your Concept Sheets.