Question

The acceleration function (in m/s²) and the initial velocity are given for a particle moving along a line. a(t) = t + 4, v(0) = 3, 0 ? t ? 11 (a) Find the velocity at time t. v(t) = m/s (b) Find the distance traveled during the given time interval. m

          The acceleration function (in m/s²) and the initial velocity are given for a particle moving along a line.
a(t) = t + 4, v(0) = 3, 0 ? t ? 11
(a) Find the velocity at time t.
v(t) = m/s
(b) Find the distance traveled during the given time interval.
m

The acceleration function (in m/s²) and the initial velocity are given for a particle moving along a line.
a(t) = t + 4, v(0) = 3, 0 ? t ? 11
(a) Find the velocity at time t.
v(t) = m/s
(b) Find the distance traveled during the given time interval.
m

Added by Lindsey P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shima Shaw

04/22/2022

Step 1

Integrating both sides, we get: \[ v(t) = \int (t + 4) dt = \frac{t^2}{2} + 4t + C \] Given that \( v(0) = 3 \), we can solve for \( C \): \[ 3 = \frac{0^2}{2} + 4(0) + C \] \[ C = 3 \] Therefore, the velocity function is: \[ v(t) = \frac{t^2}{2} + 4t + 3 \] Show more…

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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 + 4, v(0) = 3, 0 ≤ t ≤ 11 (a) Find the velocity at time t. v(t) = m/s (b) Find the distance traveled during the given time interval.