A particle starts from rest and moves in a straight line on a smooth horizontal surface. Its acceleration at time t seconds is k(4v + 1) m s-², where k is a positive constant and v ms- is e2 the speed of the particle. Given that v = when t = 1, show that 4 v =(e2t – 1). ( Take g as 10 m s?.)

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A: Given data: v0x = 19.0 m/s v0y = 11.6 m/s Need to determine maximum height y does it rise, the time…

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Q: The acceleration of a particle is defined by the relation a = − 0.8 v, where a is expressed in m/s2…

A: a=dvdt = -0.8v ln(v/u) = -0.8t v= ue-0.8t u=1m/s (given) v=e-0.8t v= dxdt =e-0.8t x= e-0.8t /(-0.8)…

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A: Given value--- v(t)=9t3−27t+12 . We have to find--- acceleration when t = 4 sec ?

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A: a. the acceleration of the particle is

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Q: A ball is thrown upward from a height of 2.2 m at an initial speed of 48 m/sec. Acceleration…

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Q: A rescue helicopter is hovering over a person whose boat has sunk. One of the rescuers throws a life…

A: Given data The initial velocity of the preserver is u = 1.8 m/s. The time interval is given as t =…

Q: At t = 0, one toy car is set rolling on a straight track with initial position 13.0 cm, initial…

A: Given, Initial Position of car 1 (x1) = 13.0 cm Initial Position of car 2 (x2) = 9.5 cm Initial…

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Q: A body moving with uniform acceleration has a velocity of 12 cm/s when its x coordinate is 30cm. If…

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Q: If a given spore is accelerated from rest to 1.23 m/s in 7.45 us, what is the magnitude of the…

A: Given,             v=1.23 m/s and t=7.45 μs=7.45×10-6sAccelaration , a=vt=1.23 m/s 7.45…

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Q: A particle moves along the x-axis with a non-constant acceleration described by a = 6t. If the…

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Q: On the earth, an astronaut throws a ball straight upward; it stays in the air for a total time of…

A: On the moon the acceleration of gravity is g/6

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: If the velocity of a particle is given by v = 10 t−5t³ , where v is in m/s and t is in seconds,…

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Q: A particle moving along the x-axis has its velocity described by the function v_x =2t2m/s=2t^2m/s,…

A: Given data: Velocity function of particle  V = 2t2 m/s Initial position x0 = 2.8 m at t = 0 s

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Q: A football is kicked from ground level with an initial velocity given by  v0x = 18.5 m/s  and  v0y…

A: Given: The horizontal component of the initial speed is 18.5 m/s. The vertical component of the…

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Q: The distance around the loop in my neighbourhood is 0.50 km. If I run exactly 3 laps of the loop,…

A: Solution .   Average velocity  V = distance covered/time.   V= r/t.

Q: Here we go again this time, d = 2.27 m. Suppose the block starts on the track at x = 0. What minimum…

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Q: A particle travels with velocity v = (8 m/s?) t - 7m/s. (a) Find the average acceleration for two…

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Q: A particle moves in the x-y plane, starting from the origin with an initial velocity of ( 4i -7.2j )…

A: Initial velocity v= (4i-7.2j)m/s  acceleration in x direction = 4i m/S2  Time t= 5s

Q: If an archer shoots an arrow straight upward with an initial velocity of 160ft/sec from a height of…

A: The height as a function of time is given, ht=-16t2+160t+8          (I) The derivative of height…

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Q: A particle moves along the x-axis. Its coordinate in meters is given by x(t) = 12t – 3.0t, where the…

A: Given data:  Particle's position as function of time x(t) = 12t - 3.0t2 Required: Time when particle…

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Q: A bird is flying due east, its distance from a tall building is given by x(t)= 32.0 + (11.1 m/s)t -…

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Q: An elevator 2.25 m high rises with a constant acceleration of 2.19 m / s2, and at the moment the…

A: This question can easily be solved by applying the basic concept of equations of motion and…

Q: A body falls vertically from the height h= 125 meters with the initial velocity equal to zero. What…

A: h = 125 m v0 = 0 m/s a = g = 10 m/s2 d' = ?

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A: Given The velocity of a particle moving along the x-axis is v(t) = A + Bt−1. The value of A is A = 2…

Q: The SpaceX Falcon 9 Launch vehicle is launched straight up at a constant acceleration of 8 m/s?. At…

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Q: A football is kicked from ground level with an initial velocity given by v0x = 20.0 m/s and…

A: Given : v0x = 20.0 m/s v0y = 12.4 m/s Acceleration due to gravity = 9.8 m/s2 Vertical Velocity at…

Q: The velocity function, in feet per second, is given for a particle moving along a straight line,…

A: Here, given the velocity function, in feet per second, is given for a particle moving along a…

Q: A particle starts from the origin at t=0 with a velocity of (16i+12j)m/s and moves in the xy plane…

A: Given:           initial velocity that is at time t=0s (u)=(16i+12j)m/s          acceleration of the…

Q: If a particle’s position is given by the expression x (t) =3.4(t²− 2x −8)³ − 5.4(t²− 2x −80)²+12)…

A: Velocity v= 51(25-2x-8)^2-108(25-2x-80) m/s.

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Special Relativity

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster than light. This interstellar speed limit has been the topic of much debate in astronomy, and also in science fiction when people consider how to fly over large distances.