A particle that moves along a straight line has velocity v(t) = t?e meters per second after t seconds. How far will it travel during the first t seconds?

Q: A particle is moving so that at any time t, its acceleration is 10t for t > or equal to 0. At the…

A: Given that,The acceleration of the particle is 10t for t ≥ 0.The particle reached at the distance of…

Q: (a) What is the cyclist's average speed, in mph, over the time interval [0, 1]? (b) What is the…

A: a) At t=0, distance=0 miles At t=1, distance= 12 miles So the average speed in the time interval…

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Q: A bomb is dropped from a helicopter hovering at an altitude of 1076 feet above the ground. From the…

A: From the given information, the value of x=500 and x0=1076 and the value of g=32fts2. Substitute…

Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

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Q: During a certain 21-hour period, the temperature at time t (measured in hours from the start of the…

A: During a certain 21-hour period, the temperature at time t (measured in hours from the start of the…

Q: a ball is thrown straight upwards from a tower (40 feet high) so that its position, s in feet, at…

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Q: The position of a particle moving along a straight line is given by s =t3-9t2+24t, where s is…

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Q: The velocity of a moving object is v(t)=2t +/t in meters per second. What is its displacement, in…

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Q: A particle that moves along a straight line has velocity v(t) = t²e-4t meters per second after t…

A: Integrae with Givenlimit

Q: Use the graph of position, h(t), shown to estimate the velocity, v(t), at t = 1s. Time (sec) in (w)…

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Q: What is the velocity at time t for a car that begins accelerating at a rate of 4 feet per second…

A: To determine the velocity from the given conditions

Q: A particle moving along a line has the position s(t) = t* – 1812 at time t seconds. What is the…

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Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

A: As the given differential equation is: dvdt=-kv2 Given conditions are:  t=0 , v=40 mst=2s, v=30 ms…

Q: A man 1.69m m tall i s walking on a horizontal street at 3.2 kph away from a vertical street light,…

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Q: A particle moves vertically (in inches) along the yaxis according to the position equation s(t) =° –…

A: We have to find value of t

Q: a car move with an initial velocity of * 50 m/s to the right, determine its position when t=15 s, if…

A: This is a problem related to newton's law of motion. Based on the general formula and concept we…

Q: A projectile is released with an initial (vertical) velocity of 110 m/s. Use the formula…

A: The velocity of particle at any time t is When the particle reach its maximum height , its velocity…

Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

A: The gradient of a scalar function at any point describes the direction in which the scalar function…

Q: With time t in seconds, the velocity of a bicycle, in feet per second, is given by At) = 4t. How far…

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Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: The forward motion of a SpaceX Dragon, t seconds after touchdown, is described by s(t) = 198t – ti,…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: A Ferrari's position at time t is given by s(t) = t3 - 9t2 + 24t 2) What is the Ferrari's velocity…

A: Given:    s(t) = t3 - 9t2 + 24 t   Velocity at t = 0

Q: A particle moves on a vertical line so that its coordinate at time t is y = t³ – 12t + 3,t > 0,…

A: Speeding up and slowing down is depend on the acceleration of particles so first find the…

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

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Q: A car travels in a straight line.  It increases its speed from 22 m/s to 28 m/s with a constant…

A: Since distance formula for constant acceleration is  v2=u2+2ax where v is final velocity, u is…

Q: Jamal is flying a kite on a string, and it is 100 ft above the ground. At the point that Jamal has…

A: Jamal is flying a kite on a string, and it is 100 ft above the ground. At the point that Jamal has…

Q: a ball is free falling from height of 200 mifind 1-the time of the ball wheureach to the ground. 2-…

A: Part(a): Given, Height=200 mg=9.8 m/s2u=0 Velocity for free falling body Let, the time be t and…

Q: If a rock is thrown vertically upward from the surface ofMars with velocity 15 m/ s  , its height…

A: Given that a rock is thrown vertically upward from surface of Mars with velocity 15 m/s. Its height…

Q: Find an equation for the instantaneous velocity v(t) if the height of an object is defined as h(t)…

A: To find: The instantaneous velocity at any point in time. Given: The height of an object is .…

Q: Assume a particle's position is given by f(t)=3/t,where t is measured in seconds and f(t) is given…

A: Assume a particle's position is given by ft=3t ,where t is measured in seconds and ft is given in…

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

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Q: Given the acceleration of an object and its initial velocity, how doyou find the velocity of the…

A: We know that the rate of change of velocity of a moving particle is known as its acceleration. Let…

Q: The velocity, v m/s of a ball thrown directly up in the air is given by ? = 20 − 10?, where t is the…

A: Soln :-         V = 20-10t            The time (t) when V is between 5 and 15 m/s.…

Q: Because of heavy rainfall, the water level in a reservoir is rising at a rate of g(t) feet per hour,…

A: Given problem :- Because of heavy rainfall, the water level in a reservoir is rising at a rate of…

Q: If the velocity of a moving object is v (t)=t- 2 in meters per second, then what is its…

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity 15 m/s, its height…

A: Given:         h=15t-1.86t2    Height of rock h(t)=25m        15t-1.86t2=25   rewrite in the form of…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 10 - 1t, where 0 <ts 3 (in…

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Q: If the position of a particle of mass m at time t seconds is given by 7= (r +1)i- 2j + ik, which of…

A: The position vector of the particle is given by, r→=t2+1i−2tj+t2k

Q: If a ball thrown into the air with a velocity of 41 ft/s, its heigh (in feet) after t seconds is…

A: Given that a ball thrown into the air with a velocity of 41 ft/s, its height (in feet) after t…

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 - 5t, where 0 ≤ t ≤ 1…

A: Here the velocity function is v(t)=13-5t   , where 0≤t≤1 (in meter per second). We have to find the…

Q: If a rock is thrown vertically upward from the surface ofMars with velocity 15m/s , its height after…

A: Given: If a rock is thrown vertically upward from the surface of Mars with velocity 15m/s, its…

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

A: Suppose that the length of rectangle is “l” and width is “w”   So according to the question, dwdt=2…

Q: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…

Q: A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32…

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