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Q. 56

Expert-verifiedFound in: Page 168

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Velocity $v\left(t\right)$ is the derivative of position $s\left(t\right)$. It is also true that acceleration $a\left(t\right)$ (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function $s\left(t\right)$, what are the units of $s(1.2)$? What are the units and real-world interpretation of $v(1.2)$? What are the units and real-world interpretations of $a(1.2)$?

Ans:

Since the distance is measured in miles, therefore the unit of $s(1.2)$ will be miles.

Again derivative of position function over time gives the velocity, therefore $v(1.2)$ will represent the velocity with unit miles per hour.

Similarly, the derivative of the velocity with respect to time gives the acceleration. Therefore the unit of acceleration is miles per hour per hour.

given,

Distance function $s\left(t\right)$

Velocity function $v\left(t\right)$

acceleration function $a\left(t\right)$

Here the function $s(1.2)$ indicates the distance covered by the object at $t=1.2$ hour. Since the distance is measured in miles, therefore the unit of $s(1.2)$ will be miles.

And the derivative of position function over time gives the velocity, therefore $v(1.2)$ will represent the velocity with unit miles per hour.

Similarly, the derivative of the velocity with respect to time gives the acceleration. Therefore the unit of acceleration is miles per hour per hour.

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