The force F on an object is the product of the mass m and the acceleration a. In this problem, assume that the mass and acceleration both depend on time t, hence so the does the force. That is, F(t) = m(t)a(t) At time t = 7 seconds, the mass of an object is 51 grams and changing at a rate of 9. At this same time, the acceleration is 8 and changing at a rate of 9. By the product rule, the force on the object is changing at the rate of Please include units in your answer (click the link for help).. To enter compound units use multiplication, division, and exponent symbols, e.g., use ft * lb for foot-pounds or m/s² for meters per second per second.

The force F on an object is the product of the mass m and the acceleration a. In this problem, assume that the mass and acceleration both depend on time t, hence so the does the force. That is, F(t) = m(t)a(t) At time t = 7 seconds, the mass of an object is 51 grams and changing at a rate of 9. At this same time, the acceleration is 8 and changing at a rate of 9. By the product rule, the force on the object is changing at the rate of Please include units in your answer (click the link for help).. To enter compound units use multiplication, division, and exponent symbols, e.g., use ft * lb for foot-pounds or m/s² for meters per second per second.

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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Question

The force F on an object is the product of the mass m and the acceleration a. In this problem, assume that the
mass and acceleration both depend on time t, hence so the does the force. That is,
F(t) = m(t)a(t)
At time t = 7 seconds, the mass of an object is 51 grams and changing at a rate of 9. At this same time, the
acceleration is 8 and changing at a rate of 9.
By the product rule, the force on the object is changing at the rate of
Please include units in your answer (click the link for help).. To enter compound units use multiplication, division,
and exponent symbols, e.g., use ft * lb for foot-pounds or m/s² for meters per second per second.

Expert Solution

Step 1

$F (t) = m (t) a (t) a t t = 7 s, m (t) = 51 g r a m s c h a n g i n g r a t e = m' (t) = 9 \frac{g}{s} a t t = 7, a (t) = 8 \frac{m}{s^{2}} c h a n g i n g r a t e = a' (t) = 9 \frac{m}{s} b y p r o d u c t r u l e \frac{d}{d t} (a . b) = a \times \frac{d b}{d t} + b \times \frac{d a}{d t}$

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