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## Calculus, all content (2017 edition)

### Course: Calculus, all content (2017 edition)>Unit 3

Lesson 11: Rectilinear motion

# Motion problems (differential calc)

## 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
What is the particle's acceleration a, left parenthesis, t, right parenthesis at t, equals, 4?
a, left parenthesis, 4, right parenthesis, equals
At t, equals, 4, is the particle speeding up, slowing down, or neither?