The acceleration function (in m/s²) and the initial velocity are given for a particle moving along a line. a(t) = t + 8, v(0) = 6, 0 sts 10 (a) Find the velocity at time t. v(t) = m/s (b) Find the distance traveled during the given time interval. m

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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The acceleration function (in m/s²) and the initial velocity are given for a particle moving along a line.

\[ a(t) = t + 8, \quad v(0) = 6, \quad 0 \leq t \leq 10 \]

(a) Find the velocity at time \( t \).

\[ v(t) = \text{\_\_\_\_\_\_\_\_\_\_\_} \, \text{m/s} \]

(b) Find the distance traveled during the given time interval.

\[ \text{\_\_\_\_\_\_\_\_\_\_\_} \, \text{m} \]
Transcribed Image Text:The acceleration function (in m/s²) and the initial velocity are given for a particle moving along a line. \[ a(t) = t + 8, \quad v(0) = 6, \quad 0 \leq t \leq 10 \] (a) Find the velocity at time \( t \). \[ v(t) = \text{\_\_\_\_\_\_\_\_\_\_\_} \, \text{m/s} \] (b) Find the distance traveled during the given time interval. \[ \text{\_\_\_\_\_\_\_\_\_\_\_} \, \text{m} \]
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