Question

Kinematics Examples:

A) A cat has a time dependent position given

by

x(t) = 4.50 m + (3.20 m/s^2) t^2 - (1.75 m/s^3) t^3

Find Velocity as function of time?

Find acceleration as a function of time?

Find the position velocity, and acceleration of the cat at t = 3.00 s?

Find average velocity and average acceleration for the 1st 3.00s?

Find the position of the cat when it first changes
direction?

B) A robot starts at X0 = 4.00m and has a time dependent velocity given by:

Vx (t) = 7.65 m/s - (3.71 m/s^3) t^2

Find the position as a function of time?

Find acceleration as a function of time?

Find the position, velocity, and acceleration at t= 2.50 s?

Find the average velocity of the robot for the first 2.50s?

Find the average acceleration of the robot from t= 1.00s to t= 2.50s ?

Is the robot speeding up or slowing down at t= 2.50s?
Explain.

C) A mouse starts at X0= +6.50 m. It is initially moving left at V0x = - 2.11 m/s. It has a time dependent acceleration given by:

ax (t) = (4.75 m/s^2) + (1.50 m/s^4) t^2

Find the position, velocity, and acceleration of the mouse at t= 5.00s?

Find the average acceleration from t= 2.00s to t= 5.00s ?

Is the mouse speeding up or slowing down at t= 0.300s?
Explain

At what time does the mouse change direction?

Answer #1

1. The position of a bird in the xy-plane is given by ?⃗ =
(3.0?−∝ ?)?̂+ ?? 2 ?̂where ∝= 1.6 ?/? and ? = 0.8 ?/? 2 . a) What
are Vx(t) and Vy(t), x and y components of the velocity of the bird
as a function of time? b) What is the bird’s net velocity at 3.0 s
(magnitude and direction)? c) What are ax(t) and ay(t), x and y
components of the acceleration of the bird as...

The position of a particle as a function of time is given by
x(t) = (t + 2t^2 + 3t^3) m. What is the average velocity between t
= 2.0 s and 5.0 s?
a. 123.0 m/s
b. 132.0 m/s
c. 213.0 m/s
d. 321.0 m/s

The position of a car as a function of time is given by x = (50
m) + (-5.0 m/s) t + (-10 m/s2) t2.
a. What are the initial position, initial velocity, and
acceleration of car? Answer: initial position ______ m; initial
velocity _____ m/s; acceleration ______ m/s2
b. What distance does the car travel during the first 1.0 s?
Answer:_____ m
c. What is the average velocity of the car between t = 1.0 s and
t =...

The position of a car as a function of time is given by x = (50
m) + (-5.0 m/s) t + (-10 m/s2) t2.
a. What are the initial position, initial velocity, and
acceleration of the car?
b. What distance does the car travel during the first 1.0 s?
c. What is the average velocity of the car between t = 1.0 s and
t = 2.0 s?

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 of a particle for t > 0 is given by →r (t) =
(3.0t 2 i ^ − 7.0t 3 j ^ − 5.0t −2 k ^ ) m. (a) What is the
velocity as a function of time? (b) What is the acceleration as a
function of time? (c) What is the particle’s velocity at t = 2.0 s?
(d) What is its speed at t = 1.0 s and t = 3.0 s? (e) What is...

2). A particle moving on the x-axis has a time-dependent
position (t) given by the equation x (t) = ct - bt^3. Where the
units of x are meters (m) and time t in seconds (s). (Hint: you
must get derivatives, you need graph paper)
(a) So that the position in x has units of meter which are the
units of the constants c and b?
Sic = 5yb = 1.Desdeti = 0satf = 3s.
(b) What is its displacement,...

1. The angle an airplane propeller makes with the horizontal as
a function of time is given by θ=(115 rad/s)t+(44.0
rad/s^2)t^2.
A. Estimate the instantaneous angular velocity at t=0.00s by
calculating the average angular velocity from t=0.00s to
t=0.010s.
B. Estimate the instantaneous angular velocity at t=1.000s by
calculating the average angular velocity from t=1.000s to
t=1.010s.
C. Estimate the instantaneous angular velocity at t=2.000s by
calculating the average angular velocity from t=2.000s to
t=2.010s.
D. Based on your results...

An electron, a neutron(which has zero charge) and a proton are
in an electric field generated by charged plates which points in
the +x direction. The three particles are sufficiently far apart
that their forces on each other are negligible. Assume also that
forces other than the electrostatic ones on the three particles are
negligible.
We know that: (Choose the correct answers)
the acceleration of the electron is in the +x direction.
the x coordinate of the electron is less...

A fragment moves in one dimension, and its position as a
function of time is given by x = (1.8 m/s)t + (−3.0
m/s2)t2.
(a) What is the fragments average velocity from t =
0.45 s to t = 0.55 s? (Indicate the direction with the
sign of your answer.)__________ m/s
(b) What is the fragments average velocity from t = 0.49 s
to t = 0.51 s? (Indicate the direction with the sign of
your answer.)___________ m/s
(c) What...

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