A biologist studying the motion of bacteria notes a bacterium at position r 1=2.2i + 3.7j − 1.2k μm (1μm = 10-6). After 7.2 seconds the bacterium is at r2 = 4.6i + 1.9k μm. Given that the acerage velocity is equal to 0.33i - 0.51j + 0.42k. Calculate the magnitude of the average velocity.

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Q: The position of a particle is: r(t) = [(4.62 m/s^2) t^2] i + (-3.38m) j + [(4.04 m/s^3) t^3] k…

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Q: The position of an object in METERS is given by X(t) = B-t" + C-t %3D Find the Sl units of the…

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Q: A particle moving in the x-y plane has a velocity at time t = 5.25 s given by (3.9i+ 6.0j) m/s, and…

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Q: the velocity of an object with time is given as in the figure below. if the values of a= 82.3,…

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Q: n object's velocity as a function of time in one dimension is given by the expression; v(t) = 2.71t…

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Q: A sports car moving at constant velocity travels 130m in 4.9s. It then brakes and comes to a stop in…

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Q: A particle leaves the origin with an initial velocity = (2.54î) m/s and a constant acceleration à =…

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Q: A particle moves in xy plane with a constant acceleration. At t = 0 the particle at = (4.0m)i +…

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Q: x (m) The given figure shows the response of a system to a step input of magnitude 1000 N. The…

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Q: (a) The velocity of a particle changes from vı = 2î + 5f -3k m/s to v2 = 5î - 7j+ 2k m/s in 2 s.…

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Q: P1. (a) A particle moves along the path whose equation is r= 2 m. If the angle 0 =r- 2t rad,…

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Q: A particle moves along a curve whose parametric equations are x = 3e-#, y = 4 sin 3t, z = 5 cos 3t…

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Q: A car is initially at rest on a straight road. The graph shows the speed of the car as a function of…

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Q: Lisa in her Lamborghini accelerates at the rate of (3.401-4.20j) m/s², while Jill in her Jaguar…

A: Given, Acceleration of Lisa aL=3.40 i^-4.20 j^ m/s2 Acceleration of Jill aJ=2.20 i^+2.60 j^ m/s2…

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Q: A particle starts from the origin of a three-dimensional coordinate system and undergoes two…

A: Given data:  Particle starts from the origin r1→= 2.0mi^ + 1.0mj^+ 3.0mk^ r2→=−1.0mi^ − 3.0mj^ −…

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^…

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

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Q: At t=0, a particle starts with an initial velocity of 10 i m/s and accelerates uniformly at (-2.0 i…

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Q: A space probe on the surface of Mars sends a radio signal back to the Earth, a distance of 7.27 ✕…

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Q: A PARTICLE MOVES ALONG THE X-AXIS. ITS POSITION VARIES WITH TIME ACCORDING TO THE EXPRESSION x = -4t…

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Q: The position of a stone thrown vertically up is y(t)=y0+ v0. t-g.t^2 where v0=10m/s is the initial…

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Q: At time t = 14 s, the velocity of a particle moving in the x-y plane is v = 0.14i + 2.87j m/s. By…

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Q: A space shuttle is fired and the position of the shuttle is given by r(t)=(2*t*t-5*t)i+…

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Q: The motion of a particle is defined by the relation x = 6r* – 21° - 12t² + 3t + 3, where x and t are…

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Q: The position of a particle for t > 0 is given by r⃗ (t) = 43.02i + 7.0 t3j + 5.0 t-2k̂ m.( a)What is…

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Q: A skateboarder travels on a horizontal surface with an initial velocity of 3.6 m/s toward the south…

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Q: the earth is approximately 1.5x10^8 km from the sun. how many minutes does it take light to travel…

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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 –