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Find a general expression for the velocity of the rock at any time t. s(t)=64-16t2,

Find a general expression for the velocity of the rock at any time t. s(t)=64-16t2,

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find a general expression for the velocity of the rock at any time t.

s(t)=64-16t2, 

Expert Solution
Step 1

Given,

The displacement vector of a rock, S(t) = 64 – 16t2

We need to find the general expression of velocity vector, v(t).

Step 2

We know that,

Velocity vector is the rate of change of displacement vector.

v(t)dS(t) dt v(t) (64-16t2 dt or, v(t) d(64) d (16t2) dt or, dt v(t) 0 32t or, v(t)32t or,
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