**Title: Calculating Velocity and Acceleration from Position Functions****Instructional Text:**Consider the position of a particle as a function of time, given by \( s = f(t) = 7t^3 + 2t + 9 \).**Problem Set:****(a) Find the velocity at time \( t \).**\[ v(t) = \quad \boxed{ \frac{m}{s} } \]**(b) Find the velocity at time \( t = 3 \) seconds.**\[ \boxed{ \frac{m}{s} } \]**(c) Find the acceleration at time \( t \).**\[ a(t) = \quad \boxed{ \frac{m}{s^2} } \]**(d) Find the acceleration at time \( t = 3 \) seconds.**\[ \boxed{ \frac{m}{s^2} } \]In these problems:- \( s(t) \) represents the position of a particle as a function of time, measured in meters (m).- \( v(t) \) represents the velocity of the particle, defined as the derivative of the position function with respect to time, measured in meters per second (m/s).- \( a(t) \) represents the acceleration of the particle, defined as the derivative of the velocity function (or the second derivative of the position function) with respect to time, measured in meters per second squared (m/s²).**Step-by-Step Solutions:**To complete each part of the problem:1. Compute the first derivative of \( s(t) \) to get the velocity function \( v(t) \).2. Compute the second derivative of \( s(t) \) to get the acceleration function \( a(t) \).3. Evaluate the velocity \( v(t) \) and acceleration \( a(t) \) at \( t = 3 \) seconds.These steps allow you to determine both the instantaneous rate of change of position (velocity) and the instantaneous rate of change of velocity (acceleration) for the particle at any given time \( t \).

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Suppose that the position of a particle is given by s= f(t) = 7t³+2t +9. (a) Find the velocity at time t. m v(t) = (b) Find the velocity at time t = 3 seconds. (c) Find the acceleration at time t. a(t) = (d) Find the acceleration at time t = 3 seconds. m

Suppose that the position of a particle is given by s= f(t) = 7t³+2t +9. (a) Find the velocity at time t. m v(t) = (b) Find the velocity at time t = 3 seconds. (c) Find the acceleration at time t. a(t) = (d) Find the acceleration at time t = 3 seconds. m

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter7: Integration

Section7.1: Antiderivatives

Problem 7YT: YOUR TURN Find an equation of the curve whose tangent line has slope f(x)=3x1/2+4 and passes through...

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