A particle moves along the x-axis so that it’s position at any time t≥0t≥0 is given by x(t)=t3−3t2+t+1x(t)=t3−3t2+t+1.  For what values of t, 0≤t≤30≤t≤3 , is the particle’s instantaneous velocity the same as its average velocity on the closed interval [0, 3]?  Your solution should clearly show all steps leading to the answer as well as justification for it.

Q: Under which of the following conditions is the magnitude of the average velocity of a particle…

A: The expression to calculate the average speed of the particle is given by, Va=DT Here, D is the…

Q: The equation of motion of a particle is s= t^3-3t , where is in meters and t is in seconds . (Assume…

A:

Q: Started at the same time from a very flat surface and 8 mm apart, (two snails are vertically…

A: Given that:x=8 mmv1=dy1dt=2 mm/sv2=dy2dt=(2+3) mm/s=5 mm/sTo determine:How fast they are separating…

Q: A particle is moving from the origin with acceleration: a=(26-12t)ms^-2 At t=4 seconds the…

A: Solution

Q: A particle moves according to the parametric equations x 19 and y = 21?, where t is in seconds and x…

A:

Q: Two masses hanging side by side from springs have positionss1 = 2 sin t and s2 = sin 2t,…

A: Here, what is to be obtained is t>0 such that Given,

Q: A falling body experiences both the gravitational acceleration g and air resistance that is…

A:

Q: The velocity of a particle constrained to move along the x-axis as a function of time t is given by:…

A: Hey, since there are multiple subparts questions posted, we will answer first three question. If you…

Q: At t=​0, a train approaching a station begins decelerating from a speed of 96 ​mi/hr according to…

A: We can find out displacement by double integrating the acceleration, Given : u = initial velocity =…

Q: A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The position of an object moving vertically along a line is given by the function ​s(t) = -4.9t2 +…

A: Givens(t) = -4.9t2 + 35t + 22

Q: he position of an object moving along a line is given by the function s(t)=−13t2+117t. Find the…

A: Average velocity is defined as the time rate of change of position of the object, i.e. total…

Q: An object's position as a function of time is given by the expression; x(t) = 14.7/(t+1) + 2.9t3 -…

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t…

A:

Q: A particle P projected from a point O on horizontal ground hits the ground after 2.4 seconds. The…

A: Given,Horizontal component of velocity, vx = 53d m/stime of flight of the ball/time taken to reach…

Q: The motion of a particle is given by V= 2t3 +3t2 +6 , where V is the velocity in m/s and t is time…

A:

Q: Consider the position function ​s(t) = -4.9t2 + 31t + 20. Complete the following table with the…

A: a)the average speed is,

Q: The velocity of an object moving along a line is given by v = 2t2 + 5 ft/s on the interval 0sts4. a.…

A:

Q: If the velocity of a particle is measured to be 0.5 in natural units(c-1), what is the velocity in…

A: Given: The velocity of the particle, v=0.5 natural unit. Require: Velocity in SI unit.

Q: Suppose that a movie is being filmed in some city. An action shot requires an object to be thrown…

A:

Q: A particle moves along the x axis according to the equation x = 1.92 + 3.03t – 1.00t“, where x is in…

A:

Q: At what time does the particle reach its maximum positive x-position using the equation, x=at2 -bt3?

A: Given data: The value of constant a is: a = 3 The value of constant b is: b = 1 The time when…

Q: At t = 0, a train approaching a station begins decelerating from a speed of 80 miles/hour according…

A: (a) . At t= 0 , the train starting deaccelerating from a speed of 80 miles/hr. So, at t= 0 , the…

Q: At a certain time a particle had a speed of 18 m/s in the positive x direction, and 2.4 s later its…

A:

Q: A particle's position is given by x = 6.00 - 15.00t + 3t², in which x is in meters and t is in…

A:

Q: A particle is fired vertically upwards and its height, h metres, after any number of seconds, t, is…

A: Solution:

Q: Under which of the following conditions is the magnitude of the average velocity of a particle…

A: Magnitude of average velocity less than average speed

Q: The x-coordinate of a particle in curvilinear motion is given by x = 4.7t - 3.1t where x is in feet…

A: Given values,

Q: An object is launched directly in the air at a speed of 64 feet per second from a platform located…

A: Basic Details The equation for the distance as a function of time is provided. Differentiate the…

Q: The motion of a dog is observed to be given by the function 7 = (1.69 m/s²) t² - [(0.4 m/s³) t³-3.61…

A: Given: The position of the dog is given as. r→=1.69 m/s2t2i^-0.4 m/s3t3-3.61 mj^…

Q: An object is snot upwards from ground level with an initial velocity of 3 meters per second; it is…

A:

Q: An iceboat sails across the surface of a frozen lake with constant acceleration produced by the…

A: Given data:  Initial velocity (Vi ) = (2.69 î - 2.98 ĵ)m/s Time (t) = 3.00 s Final velocity (Vf) =…

Q: A particle is moving along a line with position given by s(t)=t3−(9/2(t2 ))+6t−5 measured in meters,…

A:

Q: An object’s position is given by x = bt + ct3 , x in meters, t in seconds, b = 1.50 m/s and c =…

A: NOTE : According to bartleby guidelines , we can answer only first three parts of a question .For…

Q: A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s…

A: Given particle moves in s = 0.01t4-0.03t3 a) Hence the velocity of the particle is  v = dsdt = 0.04…

Q: The position of a particle along a coordinate axis at time t (in seconds) is given by s(t)=3t^2−t…

A: Given that :- s(t) =3.t2 -t  m

Q: A person skateboarding with a constant speed of 1.30 m>s releases a ball from a height of 1.25 m…

A: Given A person is skateboarding with speed V' = 1.30 m/sBall is released from height h = 1.25 mat x0…

Q: A bullet is traced with a fixed ruler and flash twice with a time interval of 2 ± 0.06 ms. If the…

A: Given: Time interval t is 2+-(0.06) ms Position 2 is 37.5+-(0.5) cm Position 1 is 23.0+-(0.5) cm

Q: A particle is restricted to move along one dimension, the x-axis. The graph below plots the velocity…

A:

Q: A particle moves according to a law of motion  s = f(t), t ≥ 0,  where t is measured in seconds and…

A:

Q: The velocity function v(t) (in meters per second) is given for a particle moving along a line. v(t)…

A:

Q: The equation for position x (meters) for a particle moving horizontally with a constant acceleration…

A: Initiial velocity of particle (v0) = 0 m/s. Initial position (x0) = 0 meters. constant acceleration…

Q: A particle moves along a line with a velocity 1 v(t) = - 3, measured in meters per t3 second. Find…

A:

Q: In an arcade video game, a spot is programmed to move across the screen according to x = 9.00t -…

A: As the question is having multiple sub parts, first three sub parts are solved.

Q: If s represents the displacement andt represents the time for an object moving with rectilinear…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Under which of the following conditions is the magnitude of the average velocity of a particle…

A: Given:  Average speed and average velocity

Q: Chapter Ten Rectilinear Motion 317 = 312 (a) the particle is initially at rest at the origin. X =S…

A: Given v=3t2+4t

Q: The function s(t) describes the motion of a particle along a line s(t)= t^2_18t+24 a) identify the…

A: To get time intervals in which the particles is moving in a negative direction is,

Relative Velocity

It is a measurement of an object with regards to the other object which is moving or stable or stationary. For example, if we are traveling in a bus and the bus is moving at speed of 50km/hr, then our speed is according to the nearby passenger on the bus is zero. According to them, we are not moving. But if one person standing on the ground or road observes us from outside of the bus, according to him we are moving at a speed of 50km/hr and the bus is also moving at a speed of 50km/hr. Now, the motion is recognized by the observer, it depends on a frame of reference or observer. This is motion called relative motion.