   Chapter 9.8, Problem 34E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Acceleration If the formula describing the distance s (in feet) an object travels as a function of time (in seconds) is s =   100   +   160 t −   16 t 2 what is the acceleration of the object when t = 4?

To determine

To calculate: The acceleration of the particle at t=4 second when the distance travelled by an object (in meters) is provided by s=100+160t16t2.

Explanation

Given Information:

The distance travelled by a particle (in meters) is provided by s=100+160t16t2 and the time is t=4 sec.

Formula used:

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

If distance covered by an object is provided by s=f(t), where t is time then its acceleration is a=f(t).

Calculation:

Consider the function,

s=100+160t16t2

Differentiate both sides of the function with respect to t,

dsdt=ddt(100+160t16t2)s=ddt(100)+ddt(160t)ddt(16t2)=ddt

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