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Motion problems (differential calc)

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

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:
Choose 1 answer:
Stuck?
Stuck?