If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

AP®︎/College Calculus AB

Course: AP®︎/College Calculus AB > Unit 4

Lesson 2: Straight-line motion: connecting position, velocity, and acceleration
Math
AP®︎/College Calculus AB
Contextual applications of differentiation
Straight-line motion: connecting position, velocity, and acceleration
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Motion problems (differential calc)

AP.CALC: CHA‑3 (EU), CHA‑3.B (LO), CHA‑3.B.1 (EK)
Google Classroom

Problem

A particle moves along the x-axis. The function v, left parenthesis, t, right parenthesis gives the particle's velocity at any time t, is greater than or equal to, 0:
v, left parenthesis, t, right parenthesis, equals, t, cubed, minus, 3, t, squared, minus, 8, t, plus, 3
What is the particle's velocity v, left parenthesis, t, right parenthesis at t, equals, 4?
v, left parenthesis, 4, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
What is the particle's acceleration a, left parenthesis, t, right parenthesis at t, equals, 4?
a, left parenthesis, 4, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
At t, equals, 4, is the particle speeding up, slowing down, or neither?
Choose 1 answer:
Stuck?
Stuck?