A space vehicle starts at an initial velocity of 100 m/s along the positive x-axis, and accelerates into space. The acceleration is a(t)= (10m/s 3 )t 2 i + 2m/s 2 j The vehicle was at the origin at the time of the launch. Find the kinematic equations for the vehicle.  Vy(t) =

Q: A bird is flying due east. Its distance from a tall building is given by  x(t)=28.0 m+(12.4…

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Q: A particle is moving in the i- j plane with an acceleration of (1 – t)į +tj where t is the time. The…

A: Given: a=1-ti+tj∫a·dt=vwhere, v is velocity…

Q: In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and…

A: given,ax(t)=-8+32tinitial velocity…

Q: particle initially is moving at a velocity with Cartesian components (5.0 m/s, 4.0 m/s) and 5.6 s…

A: Given u̅ =( 5î +4 ĵ )  v̅ = 8 î   t = 5.6 s

Q: A particle leaves the origin with initial velocity v0= 12i + 14j m/s, undergoing constant…

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Q: A car is 2.54 km west of a traffic light at t = 0 and 5.91 km east of the light at t = 6.00 min.…

A: The position of light is at origin ie (0,0). The distance coordinate of any position is expressed…

Q: A rocket is launched from rest with a time-dependent acceleration a(t) = (prt), where p = 28.50 m/s²…

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Q: A rocket is fired from rest at x = 0 and travels along a parabolic trajectory described by…

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Q: An electron is moving in a straight line with a velocity of 4.0 x 105 m/s. It enters a region 5.0 cm…

A: We have to find the electron's velocity when it emerges from given region. Given that, vi=4×105…

Q: A car is stopped at a traffic light. It then travels along a straight road such that its distance…

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Q: magnitude and direction (angle) of the position vector one second after launch

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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…

A: Write the given values with the suitable variables. t1=5.25 su=3.9i+6j m/st2=5.34 sv=4.05i+6.13j m/s…

Q: A space vehicle starts at an initial velocity of 100 m/s along the positive x-axis, and accelerates…

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Q: In the x direction, an object has an initial velocity component of 4.98 m/s and an acceleration of…

A: We are given with initial components of velocity and components of acceleration in x and y…

Q: Over a time interval of 1.54 years, the velocity of a planet orbiting a distant star reverses…

A: GivenInitial velocity is Final velocity is Time interval is We have to find total change in velocity…

Q: What is the magnitude of the horizontal displacement of a body moving at (5i + 3j) m/s after 5…

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Q: On a spacecraft two engines fire for a time of 567 s. One gives the craft an acceleration in the x…

A: Given: Timing of fire the engine (t) = 567 s. Acceleration of engine in direction x (ax) = 4.8 m/s2.…

Q: A spaceship is traveling at a constant velocity of v(t) = 300.0i m/s when its rockets fire, giving…

A: The initial velocity of the object is 300.0iˆm/s.The acceleration of the object is…

Q: The position of a honey bee (in units of meters) at t = 0.00 s is given by A = 2.00i+ 2.00j-3.00k.…

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Q: An object moves in one dimensional motion with constant acceleration a = 7.4 m/s². At time t = 0 s,…

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Q: velocity

A: Given: Acceleration of the object is given by the equation, A=(3t2+3t)i+(7t3+6)j At time = 0…

Q: An object begins to move along the y axis and its position is given by the equation y = 4t2 − 3t −…

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Q: (a) Find the velocity and position vectors as functions of time t. m/s = m (b) Find the equation of…

A: a) The particle’s velocity can be determined as, The particle’s velocity can be determined as,

Q: A spacecraft is traveling with a velocity of v0x = 5010 m/s along the +x direction. Two engines are…

A: Given data: The x-component of the initial velocity of the spacecraft, v0x=5010 m/s. The time…

Q: a particle initially at position r=(2j+3k)m moves to r=(2i+3j-2k)m in 2s. Find the magnitude of the…

A: The initial position of the particle,                                                  The final…

Q: At time t = 0 a particle at the origin of an xyz-coordinate system has a velocity vector of Vo =i+…

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Q: A computer model displays the motion of a particle on a coordinate system in real time. At time t =…

A: Velocity components: In x-direction, v = 0 In y-direction, v = 6.8 m/s Acceleration components: In…

Q: An object is moving in the x direction at 1.3 m/s when it is subjected to an acceleration given by…

A: Here, the object is moving in the x direction. So, initial velocity when written in vector form is,…

Q: On a spacecraft, two engines are turned on for 732 s at a moment when the velocity of the craft has…

A: Given The time up to which the engine turned on is t=732 s The x component of velocity is v0x =…

Q: An unidentified flying object (UFO) is observed to travel a total distance of 29000 m, starting and…

A: We have, UFO travel to a total distance of 29000 m time duration, T = 4.77 s 1 g = 9.8 m/s2

Q: Over a time interval of 1.52 years, the velocity of a planet orbiting a distant star reverses…

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Q: A space vehicle starts at an initial velocity of 100 m/s along the positive x-axis, and accelerates…

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Q: Nerve impulses in a human body travel at a speed of about 100 m/s. Suppose a person accidentally…

A: The distance travelled by the nerve impulse is d=1.6m

Q: In a time of 2.67 h, a bird flies a distance of 86.7 km in a direction 30.2 degrees east of north.…

A: Given data:  Time (t) = 2.67 h Distance (d) = 86.7 km Angle (θ) = 30.2° East of North Required: The…

Q: At time t = 13 s, the velocity of a particle moving in the x-y plane is v=0.05i + 2.54j m/s. By time…

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Q: A particle starts from the origin at t=0 with a velocity of 8.0 m/s and moves in the xy plane with…

A: Given Data :Initial speed u→ = (8 j^ ) msacceleration a→ =  3.5 i^+1.7 j^ ms2Let  i^ denotes the…

Q: On a spacecraft two engines fire for a time of 389 s. One gives the craft an acceleration in the x…

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Q: A manhwa artist draw an animation in which a dot on a computer screen has a position of r = [5.0 cm…

A: Given r→ = [5.0 cm + (3.5 m/s2) t2] i^ + (5.0 cm/s) t j^.

Q: At time t = 14 s, the velocity of a particle moving in the x-y plane is v = 0.06i + 2.21j m/s. By…

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Q: The position of a particle in the xy-plane at time t is r(t) = (e¹) + (4²¹) j. Find an equation in x…

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Q: Current Attempt in Progress A particle moving in the x-y plane has a velocity at time t = 6.82 s…

A: Given: The initial velocity of the object is 5.2i+3.7j m/s. The final velocity of the object is…

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 –