Velocity and Acceleration

Differentiate each component and get motion.

12 problems · about 23 minutes · N-VM.A.1

NameDate

Figure — use these to answer the problems

Slide the point and read the tangent slope. The velocity vector of a curve points exactly along this line.

y = 1x² + 0x + 0

the point of tangency2

Figure 1

Straightforward practice. Get the method working first.

5 problems

r(t) = ⟨t², 2t, 0⟩. What is the y-component of velocity?
Answer
2
How do velocity and speed differ?
- Velocity is a vector; speed is its magnitude.
- They are two names for the same thing.
r(t) = ⟨t³, t, 0⟩. What is the x-component of velocity at t = 2?
Answer
r(t) = ⟨t³, t, 0⟩. What is the x-component of acceleration at t = 2?
Answer
r(t) = ⟨5t, 0, 12t⟩. What is the speed?
Answer

The same ideas with more to keep track of.

3 problems

Velocity is ⟨0, 0, 0⟩ at some t. Has the particle stopped? 1 yes, 0 no.
Answer
A velocity vector of magnitude 9. What is the magnitude of the unit tangent?
Answer
r(t) = ⟨7t, −4, 0⟩. What is the y-component of velocity?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Match each quantity to its description.
Draw a line from each item on the left to its match on the right.
- Velocity
- Speed
- Acceleration
- The first derivative, a vector
- The magnitude of the first derivative, a number
- The second derivative, a vector
A particle on a circle at constant speed. Is its acceleration zero? 1 yes, 0 no.
Answer
The Drone Path
r(t) = ⟨t², 6t, 0⟩. What is the x-component of velocity at t = 5?
Answer
The Straight Run
r(t) = ⟨6t, 8t, 0⟩. What is the speed?
Answer