Question

The position of an object moving horizontally after t seconds is given by the function s =12t-t^3 , for t > 0, where s is measured in feet, with s g> 0 corresponding to positions right of the origin.

a. When is the object stationary, moving to the right, and moving to the left?

b. Determine the velocity and acceleration of the object at t=4.

c. Determine the acceleration of the object when its velocity is zero.

d. On what intervals is the speed decreasing?

Answer #1

The position function of an object moving horizontally along a
straight line as a function of timeiss(t)=t2
–3t+2,t≥0,wheresisinmetres,andtisinseconds.
Determine the velocity of the object when its position is
zero.
When is the object speeding up?
(calculus pls)

The function s(t) describes the position of a particle moving
along a coordinate line, where s is in feet and t is in
seconds.
s(t) = 3t2 - 6t +3
A) Find the anti-derivative of the velocity function and
acceleration function in order to determine the position function.
To find the constant after integration use the fact that
s(0)=1.
B) Find when the particle is speeding up and slowing down.
C) Find the total distance from time 0 to time...

The position (in meters) of an object moving in a straight
line
s(t)=√ 3t+1 −2t^2+1
where t is measured in seconds.
(a) Find the average velocity on [0,1].
(b) Find the instantaneous velocity at t=1.
(c) Find the acceleration at t=1.

The position of a car along a straight track after t seconds is
given by s =ln(3t+1)
feet. A) Find the velocity of the car after t seconds. B) Find
the acceleration of the car after t seconds

The position function of an object moving along a straight line
is given by s = f(t). The average velocity of the object over the
time interval [a, b] is the average rate of change of f over [a,
b]; its (instantaneous) velocity at t = a is the rate of change of
f at a. A ball is thrown straight up with an initial velocity of
144 ft/sec, so that its height (in feet) after t sec is given...

An
object starts with an initial velocity of -2.00i m/s. The initial
position is the origin. The constant acceleration = 4.10i + 3.20j
m/s^2.
a.) What is the initial velocity?
b.) What is the vector position at t=2.00 seconds?
c.) What is the velocity of the object at t=2.00
seconds?
d.) What is the speed of the at t=2.00 seconds?

a) Given s(t)= -10t^2+2t+5 where s(t) is the position of an
object in feet and the variable “t” is in seconds, find each of the
following:
A) Function for the velocity
B) Function for the Acceleration
C) The Velocity and Acceleration at t = 2 seconds
b) A rectangle is to have a perimeter of 60 ft. Find the
dimensions of the
rectangle such that the dimensions yield maximum area.
(please show all work possible)

Given the following acceleration functions of an object moving
along a line, find the position function with the given initial
velocity and position. a(t)=-32; v(0)=24, s(0)=0

A
particle moves in a straight line and its position is given by
s(t)=t^3 - 6t^2-36t +66, where s is measured in feet and t in
seconds. Find the intervals when the particle increases its
speed.

A particle is moving along a straight line and has acceleration
given by a(t) = 20t^3+12t^2}. Its initial velocity is v( 0 ) = 4 m
/ s and its initial displacement is s( 0 ) = 5 m. Find the position
of the particle at t = 1 seconds.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 30 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago