The displacement of a particle is given by s = 3t3 - 53t2 + 115t - 62 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 14 seconds of motion. After you have made the plots, answer the questions. Questions: At t = 3 sec, s =    ft, v =  ft/sec, a =  ft/sec2 At t = 7.7 sec, s =  ft, v =  ft/sec, a =  ft/sec2 At t = 11.5 sec, s =  ft, v =  ft/sec, a =  ft/sec2 The velocity is zero when t =  sec and when t =  sec

Q: If the car's average velocity equals the total distance it covers divided by the total time, what is…

A: We know that, The average velocity of a body is the ratio of total distance travelled by the body to…

Q: Terence is thrown from a point above the ground. The height at ground level is given by the equation…

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Q: An aircraft (A) is climbing along the straight trajectory ("dotted line") as shown in Fig.1. Q1. At…

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Q: The instantaneous speed of a particle moving along one straight line is v(t) = ate"2t where the…

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Q: An object's position as a func of time is given by ; x(t) = - 200 (( t + 1 ) ^ - 1) + 6t^2.  (Assume…

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Q: The equation of a motion of a train is given by m dv dt = mk(1 − e −t ) − mcv, where v is the speed,…

A: Solution: given thatequation of motion of trainmdvdt=mk(1-e-t)-mcvm, k and c are constants, t is the…

Q: Data Table: Dot Number Travel Timet (sec) Length of Section Around Each Dot s Average Speed Over…

A: Yes buddy you drew the perfect graph without any mistakes. The graph don't need any corrections.…

Q: At a time t = 0 s, an object is observed at position x = 0 m. Its position along the x axis is…

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Q: A particle's position along the x-axis is given by the equation;   x(t) = 1t^4 − 2t^1 + 8 where ?x…

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Q: An object's position as a function of time in one dimension is given by the expression; x(t) = 4.7t?…

A: Given data The object's position as a function of time is xt=4.7t2+6.29t+12.8. The instantaneous…

Q: If the motion of a jet after landing on a runway is shown by the a-t graph below. Note that at t = 0…

A: Dear student When acceleration is constant we can apply the equation of motions as: v = u + at Here…

Q: For a short time, the speed v of a car, in m / s, is given by v at“ + bt°, where t is the time in…

A: e is the right option

Q: The position of an object as a function of time is given by x = bt2 – ct where b = 2.0 m/s? and c =…

A: Given  x=bt2-ct

Q: The coordinate of an object is given as a function of time by x =4t2 - t, where x is in meters and t…

A: Co-ordinate of an object as a function of time x = 4t² - t³ Time interval: t = 1 s   to    t = 2 s…

Q: An object's position in the x-direction as a function of time is given by the expression; x(t) =…

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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: An object's position as a func of time is given by ; x(t) = - 200 (( t + 1 ) ^ - 1) + 6t^2.  (Assume…

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Q: A particle moves in the x-y plane with a y-component of velocity in feet per second given by v, =…

A: Answer: Given Values,

Q: An object's position as a function of time is given by the expression; x(t) = 13.9/(t+1) + 2.2t3 -…

A: Average velocity=total displacementtotal time                   ......(1)

Q: distance (m) time (sec) 0 0 25.9 51.8 77.7 104 10.1 14.3 17.5 20.2 Midpoint change in time (sec)…

A: Midpoint velocity is change in distance divided by change in time. Table. distance (m) time (sec)…

Q: As shown, the area under the velocity–time graph and between the vertical axis and time t (vertical…

A: Here,  Area under v-t graph is the displacement, let the displacement corresponding to vxi is xi and…

Q: An object has an acceleration defined by the equation a=5t+4 (m/s^2) where "t" is in seconds. The…

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Q: An objects position in the x-direction as a function of time is given by the expression: x(t)=5t^2 +…

A: The position of the object, x(t) = 5t2 + 2t The initial time, t1 = 1.15 s The final time, t2 = 2.07…

Q: The displacement of a particle is given by s = 2t³ - 42t² + 120t - 68 where s is in feet and t is in…

A: Given:s = 2t3-4zt2+120t-68Solution:The velocity as a function of time can be calculated as:v=dsdt…

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

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Q: The position of an object as a function of time is given by r = (3.2t + 1.5t2)i + (1.7t -2.0t2)jm,…

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Q: The function s(t) describes the positio of a particle moving along a coordinate line, where s is in…

A: Note : Since question has multiple sub-parts, as per guidelines we can provide solution to first…

Q: A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed…

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Q: If the motion of a jet after landing on a runway is shown by the a-t graph below. Note that att = 0…

A: Given V=430m/s and we have to find the traveled distance on the runway at time 24s.

Q: At t=0 an object starts from the origin and moves with a constant acceleration of…

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Q: he following equations give the position x(t) of a particle in four situations (in each equation, x…

A: Given, the equation of positions of the particle, x = 3t - 4x = -5t3 + 4t2 + 6x = 2t2 - 4tx = 5t2- 3

Q: A particle moves according to the law of motion s=f(t)=sint,0≤t≤2π where tt is measured in seconds…

A: Given data The expression for the distance is: s = f (t) = Sin t The time is measured in the second…

Q: The functional relation between the displacement x in meters and the time t in seconds is given by x…

A: Given:- The displacement is x  in meter and the time t in the second  The functional relation…

Q: At time t=0 s, an object is observed at x=0 m; and it’s position along the x axis follows this…

A:

Q: The position of a particle in millimeters is given by s = 30 - 13t + t? where t is in seconds. Plot…

A: Given, The position of a particle is given (in mm) by s = 30-13t+t2 , where, t is in seconds. We…

Q: The motion of a dog is observed to be given by the function = (1.78 m/s) t²i-[(0.46 m/s ) t³-3.5 m…

A: GIVEN: Position function R→ =( 1.78m/s2)t2i^ -(0.46m/s3)t3-3.5m

Q: The coordinates (in meters) of a rabbit’s position as functions of time t (in seconds) are given by:…

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Q: The coordinate of an object is given as a function of time by x = 7t – 3t2, where x is in meters and…

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Q: A particle’s velocity along the x-axis is described by v(x) = A x + B x2, where x is in meters, v is…

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Q: a(1), m/s² 10 - 1, s 1 3 - 10

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Q: A particle's position along the x-axis is given by the equation; ?(?) =1?^4 − 2?^1 + 8 where ?x is…

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Q: The displacement of a particle is given by s = 4t³ - 60t² + 100t - 58 where s is in feet and t is in…

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Q: The x component of the velocity of an object moving along the x axis is given as vy = 4t – 3t where…

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Q: The motion of a particle is defined by the equations x = (2t + t^2) m and y = (t^2) m, where t is in…

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Q: The expression x = 9.40 cos(2.25(PI)t + (PI)/2) describes the position of an object as a function of…

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Q: The position of a particle traveling along a straight line is s(t) = (C,t-C,t'+C,) ft, where t is in…

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Q: The acceleration of a race car as a function of time is a(t) = kt, where a is measured in meters per…

A: Given Data Acceleration of the car as a function of time is given as a(t)=kt At time t=0 velocity of…

Distance and Speed

The speed, distance and time relation forms the basis of study of motion. You will need these concepts in the study of Mechanics. This concept is applicable for students who are studying the following courses –