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Show that for motion in a straight line with constant acceleration $ a $, initial velocity $ v_0 $, and initial displacement $ s_0 $, the displacement after time $ t $ is$$ s = \dfrac{1}{2}at^2 + v_0t + s_0 $$

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01:32

Wen Zheng

00:36

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Missouri State University

Campbell University

Baylor University

University of Nottingham

Lectures

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So we want to show that for motion in a straight line with constant acceleration, initial velocity and initial displacement Vienna and S not, respectively, that we have our displacement after time. T. Is S. Equals one half a T squared because Vienna T plus asthma. So our constant acceleration A. Which means R a F. P function, it's just constant acceleration act. And that tells us that our velocity function is equal to 80 because aid constant plus Vienna, our velocity constant. Um in this case uh this would be plus C. But because we know that Vienna is the initial velocity will put that there. And we want to find our ask our position function that's going to be a T squared over two plus B, not T. Empty plus our initial position which is S not. So therefore we have proven what we wish to prove.

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