A vehicle travels on a straight stretch of road. Its position coordinate x (km) measured from a reference point is given by the equation  x =  4t3 + 21t2 + 18 t + 4  where t (hr) is the time measured from start of journey. After one hour, the velocity of the vehicle and the distance travelled are respectively:

Q: The coordinate of an object is given as a function of time by x = 4t² − 3t³, where x is in meters…

A: Solution: Determine the velocity of the object by differentiating the position of object with…

Q: The Shinkansen (bullet train in Japan) makes a trip from Tokyo Station to Kyoto station in 2.0 hours…

A: Given  The total distance between Tokyo Station to Kyoto station is DTotal = 460 km = 460 x 1000 m =…

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: The graph below shows the distance an object traveled over time. Distance Traveled by an Object 100…

A: Option C is the right answer  Segment Y

Q: A snowboarder starts from rest at the top of a double black diamond hill. As she rides down the…

A: Given: The displacement equation is x=0.5t3+t2+2t.

Q: At time t = 0 s, an object is observed at x = 0 m; and its position along the x axis follows this…

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Q: Leslie’s cat walks 4 meters east, 3 meters south, 2 meters west, and 9 meters north. What is the…

A:

Q: of an object (in m/s2) is given by the function a ( t ) = 5 sin ( t ). The initial velocity of the…

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Q: Q1/went for a walk one day. I walked north 6.0 km at 6.0 km/h and then west 10 km at 5.0 km/hr.…

A: As there is. Ot mentioned which part to answer therefore i am answering the first three part as per…

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: Compute your average velocity in the following two cases: (a) You walk 90.4 m at a speed of 1.98 m/s…

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Q: he velocity vx (in m/s) of an object is given by the equation vx = 4t + 3, where t is the time in…

A: Equation of velocity of object is; vx=4t+3 Part A: Displacement of object is calculated by…

Q: A motorcycle ride consists of two segments. During segment 1, the motorcycle starts from rest, has…

A: Given information: The acceleration of the motorcycle in segment 1 is, a1=1.5 m/s2 The displacement…

Q: How far has the salmon traveled? Explain the difference between your two answers

A:

Q: 2. The velocity of an object (in m/s) is given by v(t) = 4e' where t is time in seconds. Estimate…

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Q: An experiment was done where a motion sensor measured the position of a man while walking away from…

A: Given :  Time (s)  position (x)  1.0 0.234 1.2 0.287 1.4 0.326 1.6 0.388 1.8 0.430…

Q: A snowboarder starts from rest at the top of a double black diamond hill. As she rides down the…

A: Given:  x = 0.25 t3 + t2 +2tt in sec and x in feet.

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: A snowboarder starts from rest at the top of a double black diamond hill. As she rides down the…

A: given displacement equation as  x=0.25 t3 +t2 +2t where t is time in seconds position at t=5 s will…

Q: Over the course of a day, Dr. Kratzer leaves her home, travels 10 miles to Drexel, walks about 2…

A:

Q: The distance, s(t), in feet, traveled by a ball rolling down a ramp is given by the function s(t) =…

A: Given,

Q: A model car starts from rest and travels in a straight line. A smartphone mounted on the car has an…

A: The relation between time and acceleration is, Time (s) X Acceleration (m/s2) Y 0 5.95 1…

Q: When the legal speed limit for the New York Thruway was increased from 55 mi/h to 65 mi/h, how much…

A: GivenDistance travelled by motorist (D)= 450 kmwe know 1km=0.621371 milesD=450×0.621371…

Q: A car has acceleration of 4 m/s2 and starts from 1.8 m/s. What is its speed after 7.4 seconds, in…

A: Given acceleration a=4m/s2Initial speed u=1.8mstime t=7.4 s

Q: COLUMN A COLUMN B 1. This equation shows that the total displacement traveled by an object in each…

A: 1. The equation that shows the total displacement travelled by object in each amount of time is…

Q: A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10…

A:

Q: The velocity vx (in m/s) of an object is given by the equation vx = 4t + 3, where t is the time in…

A: Given data The given function is vx=4t+3 The first time is t1=1 s The second time is t2=2 s Part A…

Q: The diagram below presents the position and elapsed time of a motorbike that starts from rest and…

A: Write the expression for the average velocity. Here, x represents the displacement and t represents…

Q: The speed (m/s) an accelerating object is traveling is determined by the function v(d) = 9.8d + 8…

A:

Q: Colonel John P. Stapp, USAF, participated in studying whether a jet pilot could survive emergency…

A: (a)The acceleration of the jet is calculated as,Substitute the values,

Q: The velocity of a package traveling along the axis is shown as a function of time in the figure…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: The diagram below presents the position and elapsed time of a motorbike that starts from rest and…

A:

Q: The diagram below presents the position and elapsed time of a motorbike that starts from rest and…

A: Given Displacement of motorbike is △x=50 m Time taken is ∆t=5 s

Q: Data Table: Dot Number Travel Time t Length of Section Around Each Dot s Average Speed Over Each…

A: We can answer all the questions just by observing the above graph. (Kindly note that as per policy i…

Q: During 55 successive 1.001.00 min intervals, a runner moves at the following constant speeds:…

A:

Q: The acceleration of an object (in m/s2) is given by the function a(t)=8sin(t)a(t)=8sin(t). The…

A: a(t)=8sin(t)a(t)=8sin(t) v(0)=−10v(0)=-10 m/s

Q: time(s) position (cm) 0 49.0 5 38.0 10 43.0 15 40.0 20 60.0   A. What is the…

A: Tofind: From the data given in the table, we are required to calculate displacement, average…

Q: The velocity of a particle moving along the x-axis varies according to the expression vx = 40 – 5t²,…

A:

Q: The position as a function of time graph for an Olympic-class sprinter during a race is shown in the…

A:

Q: v(t) (feet per second) (seconds) 12 20 10 15 20 25 30 55 70 30 35 40 45 78 81 75 60 72 50 The graph…

A:

Q: The position of a particle which moves along a straight line is defined by the relation x = t3 - 6t2…

A: Given data: Position of partical x = t3 - 6t2 - 15t + 40 X in meter and t in seconds

Q: The graph shows the position of an object over a time of 75 sS. The object initially travels to the…

A: As per guidelines , only first 3 sub parts are solved here.   2.1 From graph , it can observed that…

Q: A driver traveling north slows down from 35.4m / s to 0m / s in 8.6 seconds. What is the magnitude…

A: Given: The initial velocity of the driver is 35.4 m/s in north direction. The final velocity of the…

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

A: Given:

Q: An object undergoes an acceleration as it travels along a straight, horizontal section of a track.…

A: In the given scenario object is accelerating so it will have non-uniform velocity. Consider Option A…

Q: The velocity time graph of runner is given in the graph. (a) What is the total distance covered by…

A: a) Total distance covered by the runner in 16 s: Using graph we can find the total distance as…

Q: An object moves along the x axis according to the equation x = 3.85t? 2.00t + 3.00, where x is in…

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

Q: What is the sum of 1123 and 10.3 written by scientific notation with the correct number of…

A: sum of 1123 and 10.3   1123+10.3=1133.3=1133=1.133*103answer is in 4 significant figures

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 –