Step Functions and Impulses

Switches that flip and forces that strike.

12 problems · about 23 minutes · F-IF.C.7, F-BF.B.3

NameDate

Figure — use these to answer the problems

A sharp corner like this is what a sudden change in forcing produces. The function is continuous but its slope jumps.

y = 1|x + 0| + 0

the steepness1

the moment shown1

Figure 1

Straightforward practice. Get the method working first.

5 problems

A mass moving at 3 receives an impulse adding 4 to its velocity. What is the new velocity?
Answer
2
What does an impulse change instantly?
- The velocity, while the position stays where it was.
- The position, while the velocity is unchanged.
A step function turning on at t = 3. What is its value at t = 5?
Answer
A step function turning on at t = 3. What is its value at t = 1?
Answer
An impulse applied to a mass. Does the position jump? 1 yes, 0 no.
Answer

The same ideas with more to keep track of.

3 problems

An impulse applied to a mass. Does the velocity jump? 1 yes, 0 no.
Answer
A mass at rest receives an impulse giving velocity 8. What is its velocity immediately after?
Answer
A mass moving at 2 receives an impulse adding 6 to its velocity. What is the new velocity?
Answer

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

4 problems

Sort each quantity by whether an impulse changes it instantly.
Write each item under the heading it belongs to: Velocity · Position · Momentum · The location of the mass
Changes instantly
Stays the same through the impulse
A step function turning on at t = 0. What is its value at t = 10?
Answer
The Kick
A mass at rest at position 3 receives an impulse. What is its position immediately after?
Answer
The Switch
A step function turning on at t = 4. What is its value at t = 2?
Answer