# calculus

a particle moves along a number line measured in cm so that its position at time t sec is given by s=72/(t+2) +k, k is a constant and t>=0 seconds.
(a) Find the instantaneous velocity of the particle at t=4 seconds
(b) Find the acceleration of the particle when t =4 seconds
(c) If we know the particle is at s=20 when t=4sec, use your answer from part( a) to approximate the position of the particle at t=4.5 sec.

1. a)v(4)=-2 seconds
b)a(4).67

2. i don't know the answer for partc.

3. is answer a and b correct

4. a) and b) are correct

for c)
sub in the given values
20 = 72/6 + k
20 = 12 + k
k = 8

so now you know
s= 72/(t+2) + 8
when t = 4/5
s = 72/4.5 + 8 = 24

posted by Reiny
5. Part (a) is correct, and (b) is correct to 2 decimal places.

For part (c), you can make use of the approximation formula
f(t0+h)=f(t0)+h*f'(t0) approximately, and when h is relatively small.
t0=4
f(t0)=20,
f'(t0)=-2
h=4.5-t0=0.5
f(t0+h)=f(4.5)=20+(-2)*0.5=19 (approx.)

Check by initial conditions:
f(4)=20
substitute in s(t) to get
20=72/(4+2)+k=12+k
=> k=8
So
f(t)=72/(t+2)+8
f(4.5)=72/(4.5+2)+8
=19.077...
So approximation above is reasonably accurate.

posted by MathMate

## Similar Questions

A particle moves along a line so that its position at any time t >= 0 is given by the function -t^3 + t^2 + 5t + 3, where p is measured in feet and t is measured in seconds. 1. Find the displacement during the first four
2. ### Calculus

1) A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(2t). Find the acceleration of the particle when the velocity is first zero. 2) The driver of a car traveling at 50 ft/sec suddenly
3. ### Calculus

Sorry this is really long. Just wondering how I would do each of these A particle is moving with velocity v(t) = t^2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between
4. ### Calculus

The position of a particle moving on a horizontal line is given by s(t)=2t^3-15t^2+24t-5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? b: What is the average velocity of the
5. ### Calculus

A particle moves along a line so that its posistion at any t is greater than or equal to 0 is given by the function s(t)= t^3-8t+1, where s is measured in feet and t is measured in seconds. a) find the displacement during the
6. ### Calculus

A particle moves along a horizontal line so that at any time t its position is given by x(t)=cost-t. Time is measured in seconds and x is measured in meters. a.) Find the velocity as a function t. Use your answer to determine the
7. ### Calculus

The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 5/t2, where t is measured in seconds. Find the velocity of the particle at times t = a, t = 1, t = 2, and t = 3. (a) Find
8. ### calculus

A particle moves along a number line such that its position s at any time t, t(greaterthan or equal to), is given by s(t)=2t^3-15t^2+24t+1. A) Find the average velocity over the time interval [1,2]. B) Find the instantaneous
9. ### Calculus

The displacement (in meters) of a particle moving in a straight line is given by s=2t^3 where is measured in seconds. Find the average velocity of the particle over the time interval [10,13]. the average velocity is 798 What is
10. ### math

The displacement (in meters) of a particle moving in a straight line is given by s = 4 t^3 where t is measured in seconds. Find the average velocity of the particle over the time interval [ 7 , 9]. Find the (instantaneous)

More Similar Questions