### Home > CALC > Chapter 3 > Lesson 3.1.2 > Problem 3-32

Jasmin rolled a ball down a very steep ramp and got the distance function *s*(*t*) = 2.3*t*^{2} , where *t* is measured in seconds and *s*(*t*) is measured in feet. Sketch a graph of her distance function on your paper. Then, carefully approximate the speed of the ball at *t* = 3 seconds. 3-32 HW eTool (Desmos). Homework Help ✎

The velocity/speed at *t* = 3 should be the same as the IROC (or slope of the tangent line) at *t* = 3.

*v*(3) = 13.8 ____________ don't forget units!

Find the slope function of *s*(*t*) by finding the IROC at *x* = 3:

1. Evaluate when *f*(*x*) = *s*(*t*) = 2.3*t*^{3}.

2. Expand and simplify the numerator.

3. Factor out an *h* from the numerator.

4. 'Cancel out' the *h* from the fraction.

*v*(3) can also be found with Power Rule:*s*(*t*) = 2.3*t*^{2}*v*(*t*) = 4.6*t**v*(3) = _____________

Use the eTool below to help solve the problem.

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