Question

The acceleration function for a particle moving along a line is \(a(t) = 2t + 2\). The initial velocity is \(v(0) = -15\). Then: The velocity at time \(t\), \(v(t) = 195\) The distance traveled during the time interval \([0, 5]\) is equal to = 195

          The acceleration function for a particle moving along a line is \(a(t) = 2t + 2\). The initial velocity is \(v(0) = -15\). Then:
The velocity at time \(t\), \(v(t) = 195\)
The distance traveled during the time interval \([0, 5]\) is equal
to = 195

The acceleration function for a particle moving along a line is a(t) = 2t + 2. The initial velocity is v(0) = -15. Then:
The velocity at time t, v(t) = 195
The distance traveled during the time interval [0, 5] is equal
to = 195

Added by Gloria M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Drew Scalzo

08/20/2023

Step 1

To find the velocity function, we need to integrate the acceleration function with respect to time. Given: a = 2t + 2 Integrating both sides with respect to t, we get: ∫a dt = ∫(2t + 2) dt Integrating, we get: v(t) = t^2 + 2t + C where C is the constant of Show more…

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Texts: The acceleration function for a particle moving along a line is a = 2t + 2. The initial velocity is v0 = -15. Then, The velocity at time t, v(t), is 195. The distance traveled during the time interval [0,5] is equal to 195.