Each integration constant needs its own starting value.

You integrate an acceleration function once. What do you get?

• Position, with both constants already fixed
• Velocity plus one unknown constant
• Force plus two unknown constants

Acceleration stays constant at value a. After two integrals, the position is what?

• Starting position plus starting velocity times t plus a times t squared
• Starting velocity plus starting position times t plus half a times t squared
• Starting position plus starting velocity times t plus half a times t squared

What does the area under the acceleration curve between two times tell you?

• The distance travelled over that stretch of time
• The starting position of the trip
• The change in velocity over that stretch

You know a(t) but never wrote down the starting velocity. What happens?

• You get a family of possible velocities
• You still get one exact velocity, just as before
• You get the position function directly

A sled coasts with velocity v(t) = 4.0 - t squared/4 meters per second. The math gives negative velocity after 4 seconds. What does that mean?

• The sled stays stopped at that spot for good
• The sled slides back toward where it started
• The slowing force suddenly turns positive

A particle starts from rest at the origin while its acceleration falls with time. What fixes the two constants?

• The acceleration function fixes both by itself
• Zero starting position fixes the first, and zero starting velocity fixes the second
• Zero starting velocity fixes the first, and zero starting position fixes the second

A trolley moves with v(t) = 9 - t squared meters per second from the origin. It stops after 3 seconds, 18 meters along. A student says the model proves the trolley rests there forever. What is the mistake?

• Past 3 seconds the equations give negative velocity
• The stopping distance should have come out as zero meters
• The velocity function never quite reaches zero in this model