Velocity and acceleration as derivatives

Science · Forces & Motion · ages 18-19

Name ______________________ Date ____________

With s(t) equal to t cubed plus 2t, what is v(t)?
- 6t
- t squared plus 2
- 3t squared + 2
If s(t) is position, what are velocity and acceleration?
- Velocity is the derivative of position, acceleration of velocity
- Position is the derivative of velocity
- Both equal the second derivative of time
What does the sign of velocity tell you?
- How fast the speedometer climbs
- The direction along the axis
- The value of acceleration
For r(t) equal to the pair t squared and 3t, what is the acceleration vector?
- The pair 2t and 3
- The pair 2 and 0
- The pair 2t and 0
With s(t) equal to t cubed plus 2t, what is the acceleration at t equal to 2?
Answer: ______________
For the same r(t), what is the speed at t equal to 2?
Answer: ______________
Sam says the constant acceleration equations still apply when acceleration is 6t.
Circle one: True False
With a(t) equal to 6t, why do the constant acceleration equations stop applying?
- Because acceleration changes with time
- Because velocity is always 14
- Because motion needs two dimensions

Answer key

For grown-ups. Fold this page away before handing over the rest.

3t squared + 2 · Differentiate term by term: t cubed gives 3t squared and 2t gives 2.
Velocity is the derivative of position, acceleration of velocity · Each step differentiates the last: position to velocity to acceleration.
The direction along the axis · Positive points one way along the axis and negative the other.
The pair 2 and 0 · Differentiate each component twice: t squared gives 2 and 3t gives 0.
12 · Differentiating twice gives a(t) equal to 6t, and 6 times 2 is 12.
5 · Velocity at 2 is the pair 4 and 3, whose length is 5.
False · Sam is wrong: with acceleration depending on time, those formulas stay on the shelf.
Because acceleration changes with time · Those equations assume fixed acceleration, so a changing 6t breaks them.