Question

A particle is moving along a straight line, and its position is defined by s = (t2 - 6t +6) m. At t=6 seconds, find the following : a. the acceleration of the particle b. The average speed c. the average velocity

Answer #1

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...

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.

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/
and its initial displacement is s(0) = 5 ms. Find the position of
the particle at t = 1 seconds.
10 m
5 m
11 m
4 m
2m

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.

The displacement (in centimeters) of a particle moving back and
forth along a straight line is given by the equation of motion
s = 4 sin(πt) + 5
cos(πt),
where t is measured in seconds. (Round your answers to
two decimal places.)
(a) Find the average velocity during each time period.
(i) [1, 2] cm/s
(ii) [1, 1.1]
cm/s
(iii) [1, 1.01]
m/s
(iv) [1, 1.001]
(b) Estimate the instantaneous velocity of the particle when
t = 1.

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...

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.

A particle moves along the x axis. It is initially at the
position 0.150 m, moving with velocity 0.080 m/s and acceleration
-0.340 m/s2. Suppose it moves with constant acceleration for 5.60
s. (a) Find the position of the particle after this time. (b) Find
its velocity at the end of this time interval. Next, assume it
moves with simple harmonic motion for 5.60 s and x = 0 is its
equilibrium position. (Assume that the velocity and acceleration is...

The displacement (in centimeters) of a particle moving back and
forth along a straight line is given by the equation of motion
s = 3 sin(πt) + 4
cos(πt),
where t is measured in seconds. (Round your answers to
two decimal places.)
(a) Find the average velocity during each time period.
(i) [1, 2]
cm/s
(ii) [1, 1.1]
cm/s
(iii) [1, 1.01]
cm/s
(iv) [1, 1.001]
cm/s
(b) Estimate the instantaneous velocity of the particle when
t = 1.
cm/s

If the velocity at time t for a particle moving along a
straight line is proportional to the square root of its position
x, write a differential equation that fits this
description

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 24 minutes ago

asked 31 minutes ago

asked 38 minutes ago

asked 40 minutes ago

asked 51 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago