Question

Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position. $$a(t)=-0.01 t ; v(0)=10 ; s(0)=0$$

          Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position.
$$a(t)=-0.01 t ; v(0)=10 ; s(0)=0$$

Added by Diane J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

07/31/2023

Step 1

$$v(t) = \int a(t) dt = \int -0.01t dt$$ Now, integrate: $$v(t) = -0.005t^2 + C$$ We are given the initial velocity, v(0) = 10. Use this to find the constant C: $$10 = -0.005(0)^2 + C$$ $$C = 10$$ So, the velocity function is: $$v(t) = -0.005t^2 + 10$$ Show more…

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Find the position and velocity of an object moving along a straight line with the given acceleration, initial velocity, and initial position. $$a(t)=-0.01 t ; v(0)=10 ; s(0)=0$$