13.1.A.1Multiple Choice
What is the translational kinetic energy of a 4 kg object moving at 5 m/s?
Select A, B, C, or D to check your answer.
Directions:Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions 1–6 go through 3.1.A.1–A.3 in order; questions 7–20 mix them. Use g = 10 m/s² only if a problem requires gravity — most of these do not. Round decimals to the nearest hundredth unless noted otherwise.
What is the translational kinetic energy of a 4 kg object moving at 5 m/s?
Select A, B, C, or D to check your answer.
A 0.50 kg ball has 18 J of kinetic energy. (a) Find its speed. (b) If the mass were doubled but the speed stayed the same, what would the new kinetic energy be? (c) If instead the speed were doubled but the mass stayed the same, what would the new kinetic energy be?
A 2 kg ball moves with velocity +6 m/s (east). After bouncing elastically off a wall, it moves with velocity −6 m/s (west). How does its kinetic energy after the bounce compare to its kinetic energy before?
Select A, B, C, or D to check your answer.
Two identical 3 kg carts move toward each other on a frictionless track: Cart A at 2 m/s east, Cart B at 2 m/s west. (a) Find each cart's kinetic energy. (b) Explain why you cannot add the carts' velocities as vectors to find the system's total kinetic energy. (c) Find the total kinetic energy of the two-cart system.
| Object | mass (kg) | speed (m/s) | K (J) |
| Cart A | 3 | 2 | 6 |
| Cart B | 3 | 2 | 6 |
A 70 kg passenger walks forward at 1.5 m/s inside a train car that itself moves at 20 m/s relative to the ground (same direction). A seated passenger on the train (Observer I) and a person standing on the ground (Observer II) each measure the walking passenger's kinetic energy. Which statement is correct?
Select A, B, C, or D to check your answer.
A 60 kg skater stands still relative to a 1200 kg boat that drifts at 3 m/s relative to the shore. (a) Find the skater's kinetic energy as measured by a person standing on the boat. (b) Find the skater's kinetic energy as measured by a person standing on the shore. (c) Explain why these two values differ even though the skater's own motion relative to the boat hasn't changed.
An object's speed triples while its mass stays the same. By what factor does its kinetic energy change?
Select A, B, C, or D to check your answer.
The table gives the mass and speed of four objects. (a) Find the kinetic energy of each. (b) Rank the four objects from least to greatest kinetic energy.
| Object | mass (kg) | speed (m/s) |
| P | 2 | 4 |
| Q | 3 | 3 |
| R | 1 | 6 |
| S | 5 | 2 |
A 1 kg object moves with a velocity that has components vx = 3 m/s and vy = 4 m/s (so its speed is 5 m/s). A student finds the object's kinetic energy by computing ½mvx2 and ½mvy2 separately and adding them. Is this a valid way to find the total kinetic energy?
Select A, B, C, or D to check your answer.
Train C moves east at 12 m/s. A 1.5 kg bag sits at rest on Train C's floor, moving along with the train. (a) Find the bag's kinetic energy as measured by a passenger on Train C. (b) Find the bag's kinetic energy as measured by a person standing still on the ground. (c) If instead the person on the ground were walking east at 2 m/s, what kinetic energy would they measure for the bag?
An object moving at 10 m/s has 250 J of kinetic energy. What is its mass?
Select A, B, C, or D to check your answer.
The graph shows kinetic energy K versus speed v for a fixed mass of 2 kg. (a) Identify the shape of the curve and explain why it has that shape. (b) Use the equation to find K at v = 6 m/s. (c) Explain what would happen to the shape of the curve if the mass were larger instead.
A 1500 kg car travels at −25 m/s (that is, in the negative direction on a coordinate axis). What is its kinetic energy?
Select A, B, C, or D to check your answer.
Train D moves north at 18 m/s. Train E moves south at 6 m/s on a parallel track. A 3 kg package sits at rest on Train D's floor, moving along with Train D. (a) Find the package's kinetic energy relative to Train D. (b) Find the package's velocity relative to Train E (taking north as positive). (c) Find the package's kinetic energy relative to Train E.
Which combination of SI base units is equivalent to the joule, the unit of kinetic energy?
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A 6 kg object at rest explodes into two fragments: a 2 kg fragment that flies off at +12 m/s and a 4 kg fragment that flies off at −6 m/s, so that the system's total momentum stays at zero (2(12) + 4(−6) = 0, as momentum conservation requires). (a) Find the kinetic energy of each fragment. (b) Find the total kinetic energy of the system after the explosion. (c) Explain why this total isn't zero even though the total momentum is.
For a fixed speed, how does a graph of kinetic energy K versus mass m appear?
Select A, B, C, or D to check your answer.
A 1200 kg car is parked (at rest) on the ground. A second car drives past at 15 m/s. (a) Find the parked car's kinetic energy as measured by a person standing on the ground. (b) Find the parked car's kinetic energy as measured by the driver of the moving car. (c) Can either of these values be negative? Explain.
Three identical 5 kg objects move at the same speed, 4 m/s, but in three different directions: one moves north, one moves east, and one moves southwest. Which one has the greatest kinetic energy?
Select A, B, C, or D to check your answer.
A 1000 kg car is driving at 20 m/s on a highway. A motorcycle traveling in the same direction at 30 m/s passes the car. (a) Find the car's kinetic energy as measured by someone standing on the side of the road. (b) Find the car's kinetic energy as measured by the motorcyclist. (c) Is either of these two values negative or direction-dependent? Explain using the scalar nature of kinetic energy. (d) If the car's speed relative to the ground were instead cut in half, what would its new kinetic energy be, relative to the ground?