AP Physics 1 · Unit 1 · Kinematics

Vectors and Relative Velocity Practice Problems

Add displacements in two dimensions and describe motion from different reference frames. Work with survey routes, a moving train, and river crossings with and without downstream drift.

13 questions6 conceptual · 7 calculation

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Simulation scene from the Vectors and Relative Velocity lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Keep the direction and the reference frame

Resolve and combine vectors

Use horizontal and vertical components to add several displacements or reconstruct an unknown vector. Interpret angles measured from north as well as from east.

Change reference frames

Combine a person’s velocity relative to a train with the train’s velocity relative to the ground. Name the reference frame for each quantity.

Plan a river crossing

Find crossing time and downstream drift when aiming across the water. Compare that route with an upstream heading chosen to reach the opposite bank directly.

A question from this set

Does addition order matter?

Two displacement vectors are placed head to tail. If their order is reversed, with each vector’s magnitude and direction unchanged, what happens to the resultant?

The resultant changes direction because the first vector changes.
The resultant is unchanged, although the route can be different.
The resultant’s magnitude becomes the sum of the two magnitudes in every case.

Try it in the practice set

The same two vectors can be placed head to tail in either order.

Key ideas

Components keep different directions separate

Add like components

Horizontal components add to give the horizontal resultant; vertical components give the vertical resultant. Reversing addition order changes the route but leaves the vector sum unchanged.

A velocity belongs to a frame

For river motion, boat velocity relative to the ground is boat velocity relative to the water plus water velocity relative to the ground. Crossing time depends on the across-river component.

See the physics

Compare vector routes and moving frames

After checking your work, switch the order of a displacement route or compare train and river trials. Use the recorded paths and component arrows to relate the motion in each reference frame.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for vectors and relative velocity?

Begin with a conceptual question, then work through the calculations.

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