Question

A particle moves along a line with velocity v(t)= t-ln(t^2+1). What is the maximum velocity on the interval [0,2]?

Answer #1

UPVOTE PLEASSEEE D

A particle that moves along a straight line has velocity v ( t )
= t^2e^− 2t meters per second after t seconds. How many meters will
it travel during the first t seconds (from time=0 to time=t)?

A particle travels along a straight line with a velocity
v=(12−3t^2) m/s , where t is in seconds. When t = 1 s, the particle
is located 10 m to the left of the origin.
Determine the displacement from t = 0 to t = 7 s.
Determine the distance the particle travels during the time
period given in previous part.

Question 4.
An object moves in a straight line with a velocity of v(t) = ((t
− 2)(t − 3)).
a) What is the total displacement on the time interval [0,
5]?
b) What is the total distance traveled on the time interval [0,
5]?

The velocity function (in meters per second) is given for a
particle moving along a line.
v(t) =
t2 − 2t −
8, 1 ≤ t ≤ 5
(a) Find the displacement. (m)
(b) Find the distance traveled by the particle during the given
time interval. (m)

A mass (m) moves along the x-axis with velocity 2v. Another
particle of mass (2m) moves with velocity v along the y-axis.
1) If the two objects collide inelastically and merge, how much
kinetic energy is lost to heat?
2) If instead they collide elastically and it turns out that m
still moves purely along the x-axis, what is it's velocity in the
final state?
It may help to find the velocities of these particles in the
center of mass...

A particle of mass, m, in an isolated environment moves along a
line with speed v whilst experiencing a force proportional to its
distance from the origin.
a) Determine the Langrangian of the system
b) Determine the Hamiltonian of the system
c) Write down Hamilton’s equations of motion for the particle d)
Show that the particle executes simple harmonic motion

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.

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

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.

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

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