The vector position of a particle varies in time according to the expression r → = 3.00 i ^ − 6.00 t 2 j ^ , where r → is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the acceleration of the particle as a function of time. (c) Calculate the particle’s position and velocity at t = 1.00 s.
The vector position of a particle varies in time according to the expression r → = 3.00 i ^ − 6.00 t 2 j ^ , where r → is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the acceleration of the particle as a function of time. (c) Calculate the particle’s position and velocity at t = 1.00 s.
Solution Summary: The author explains the expression for the velocity as a function of time, and the formula for calculating acceleration.
The vector position of a particle varies in time according to the expression
r
→
=
3.00
i
^
−
6.00
t
2
j
^
, where
r
→
is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the acceleration of the particle as a function of time. (c) Calculate the particle’s position and velocity at t = 1.00 s.
A particle’s acceleration is (4.0iˆ+3.0jˆ)m/s2.(4.0i^+3.0j^)m/s2. At t = 0, its position and velocity are zero. (a) What are the particle’s position and velocity as functions of time? (b) Find the equation of the path of the particle. Draw the x- and y-axes and sketch the trajectory of the particle.
The vector position of a particle varies in time according to the expression r = 9.00 î - 8.00t? ĵ where r is in meters and t is in seconds.
(a) Find an expression for the velocity of the particle as a function of time, (Use any variable or symbol stated above as necessary.)
m/s
(b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.)
a =
m/s2
(c) Calculate the particle's position and velocity at t = 3.00 s.
ř =
m/s
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Problem 2: The position of a particle is given by the following expression, where t is time
measured in seconds: r(t) = [(3.65 m/s?)f²]į+ (-4.23 m)j + [(4.48 m/s³)r*]k.
Part (a) What is the magnitude of the velocity of the particle, in m/s, at t = 0.00 s?
Part (b) What is the magnitude of the velocity of the particle, in m/s, at t = 1.65 s?
Part (c) What angle, in degrees, does the velocity of the particle make with the +z axis at t =
1.65 s?
Part (d) What is the magnitude of the average velocity, in m/s, betweent = 0.00 s and t = 1.65
s?
Part (e) What angle, in degrees, does the average velocity between t = 0.00 s and t = 1.65 s
make with the z axis?
Chapter 4 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
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