   Chapter 9.8, Problem 33E ### 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 A particle travels as a function of time according to the formula s =   100   +   10 t +   0.01 t 3 where s is in meters and t is in seconds. Find the acceleration of the particle when t = 2.

To determine

To calculate: The acceleration of the particle at t=2 second when the distance travelled by a particle (in meters) is provided by s=100+10t+0.01t3.

Explanation

Given Information:

The distance travelled by a particle (in meters) is provided by s=100+10t+0.01t3 and the time is t=2 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+10t+0.01t3

Differentiate both sides of the function with respect to t,

dsdt=ddt(100+10t+0.01t3)s=ddt(100)+ddt(10t)+ddt(0.01t3)=ddt(100)+10ddt(t)+0

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