Calculus
posted by Raul .
The position of a particle moving on a horizontal line is given by s(t)=2t^315t^2+24t5, 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 particle on the interval [0,2]?Indicate units of measure
c: Find a formula for the instantaneous velocity of the particle.
d: When is the particle at rest?
e: When is the particle moving to the right? When is it moving to the left?
f: At t=2 seconds, is the particle moving away from the origin or towards the origin?
h: What is the average acceleration of the particle on the interval [0,2]?
i: Find a formula for the instantaneous acceleration of the particle.
j: At t=2 seconds, is the particle slowing down or speeding up?

a) sub in t = 0
b) avg vel = (s(2)  s(0) )/(20) = ...
c) s ' (t) = 6t^2  30t + 24
d) particle is at rest, when velocity = 0 , that is ...
6t^2  30t + 24 = 0
t^2  5t +4 = 0
(t1)(t4) = 0
when t = 1 or when t = 4
f) sub t=2 into the derivative of c)
if it is positive, > to the right
if it is negative, > to the left
e) same steps as b) except use the velocity expression
you do some of them. 
How do you do E on this problem??
Respond to this Question
Similar Questions

Calculus
A particle moves on a vertical line. Its position, s, in metres at t seconds is given by s(t) = t^3  9t^2 + 24t, t>0/ I found the velocity and acceleration functions. s'(t) = 3t^2  18t + 24 s''(t) = 6t18 b) When is the particle … 
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^315t^2+24t+1. A) Find the average velocity over the time interval [1,2]. B) Find the instantaneous velocity … 
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 … 
Calculusparticle motion
1. A particle is moving on the xaxis (or any number line) Its position x(t), or distance from the origin, at the time t is given by x(t)=4t^316t^2+15t. t is greater than or equal to 0 a.) Where is the particle when it is at rest? 
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 the … 
Physics
A particle is moving along a straight line and its position is given by the relation x=( t36t215t+40)mm. Find: (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration … 
physics
A particle is moving along a straight line and its position is given by the relation x=( t36t215t+40)mm. Find: (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration … 
physics
A particle is moving along a straight line and its position is given by the relation x=(t3 6t2 15t+40) m FIND a) The time at which velocity is Zero, b) Position and displacement of the particle at that point. c) Acceleration for … 
Calculus
The position of a particle on the xaxis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for 1 ≤ t ≤ e? 
Calculus
1) A particle is moving along the xaxis 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 applies …