The displacement (in meters) of a particle moving in a straight line is given by s = t2 - 9t + 17, where t is measured in seconds. (a) Find the average velocity over each time interval. (i) [3, 4] 1 x m/s (ii) [3.5, 4] 2 |× m/s (iii) [4, 5] 2 X m/s (iv) [4, 4.5] 4 X m/s (b) Find the instantaneous velocity when t = 4. 2-1 x m/s

Q: A particle is moving along the x-axis so that its position at time t≥0 is given by the equation…

A:

Q: Find the equation of the tangent and normal line of the function f(x) = V2x – 1 at the point (5, 3).

A: fx = 2x-1     , 5,3f'x = ddx2x-1     = ddx2x-112        = 122x-1ddx2x-1        = 222x-1 = 12x-1∴f'5…

Q: Find all points (x,y) on the graph of f(x) = 2x3 + 1 with tangent lines perpendicular to the line y=…

A:

Q: A particle moves along a line so that its velocity is given by v(t)=−t^3+2t^2+2^(−t) t≥0. For what…

A:

Q: The velocity function (in meters per second) for a particle moving along a line is given by v(t) =…

A: Given, v(t)=t3-2t2   Interval [a,b]=[-2,3]

Q: 1. (a). Find the linear approximation to f(x) = VT at a 81, (b). use it to approximate 85. (c).…

A:

Q: Find the slope of the line tangent to the curve x - 3xy + 4x = 2 at x = 1. -5/3 O 2/3 O 1/3 O 4/3

A: The given curve is: x3-3xy+4x=2 We need to find the slope of the line tangent to the given curve.…

Q: The equation of the tangent line to the graph of f(x) = Vx+1 At the indicated point (3,2) is:…

A: By using the derivative and slope intercept form required tangent equation is :

Q: 4. Find an equation of the line tangent to g(x) = 3x² - x +1 at x= 1.

A: Given function

Q: A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over…

A: A particle is moving along the y-axis its position is given by y(t)=t3-6t2+9t      at…

Q: 10. (a) Find an equation for the line tangent to f(x) = x³ + 4x² at the point x = 1.

A:

Q: Suppose the velocity function of a particle is given by y = 2 – t - t2 at any time t ( time is in…

A:

Q: For the graph y = f(x) = 3x² – x + 2 (i) (ii) Q3. %| - Find the average rate of change of y w.r.t x…

A:

Q: Suppose a stone is dropped from a height of 200 ft. Its position at time t is s(t)=-4r +200. Find…

A:

Q: 4. Find the equation of a line tangent to f (x) = –x² – 4x at x = -1.

A:

Q: ,2_2t A particle moves along a straight line with a velocity v(t) = t²e²¹ meters per second after t…

A:

Q: Let v(t) = t2 -2t-5 be the velocity function for a particle moving along a straight line. Here,…

A:

Q: Suppose the position function of a moving object is given by s (æ) = Væ. Then the average velocity…

A: Given that: To find:

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 4t + 14 for time t > 0. If the…

A: Convert velocity into distance and time

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 – 60t.…

A: v(t)=3t2-60t,    t≥0the particle is moving to the right whenv(t)>03t2-60t>03t(t-20)>0

Q: 1. (a). Find the linear approximation to f(x) = VT at r = 81, (b). use it to approximate V85. (c).…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occur f(x, y)…

A: Topic- Vectro

Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: For the given velocity  v(t) = 10t +12 for t>=0 if the position is x =2  at time t = 0  Position…

Q: The velocity of a partical moving along x axis is defined by               v= kx3-4x2+6x where v is…

A:

Q: Jim is driving at a constant 75.0 mi/hr (33.5 m/s) along a straight section of Route 3 North. The…

A:

Q: (4) Find the equation of the line tangent to f(x) = 12√ - 2² at the point (4,8).

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 - 3t, where 0<t < 4 (in…

A:

Q: 2. Find the slope of the tangent line to f(x)=V4-V+5 at the point where x 4.

A:

Q: 4) Find the equation of the line tangent to h(x) = (2-x)(x³ +4x-4) at x=1.

A:

Q: II. FIND THE EQUATION OF THE LINE TANGENT TO_f(x) 1. f(x)= (x+1)' (2x +3)² at x=-2

A:

Q: What is the approximate value of the first derivative of S(x)=-0.1x*-0. 15x-0.5x-0.25x-1. 2 at…

A:

Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

A:

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

A:

Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = 10t(4 − t) (t +…

A: The given data isVt=10t4-tt+1t-7m/s.To find:The distance travelled by particle over interval t∈0,6.

Q: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

A: We will use formula for the Displacement and distance in terms of Velocity function

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: 5. Let f(x, y) = x² - y² x² + y² a. In which direction should you move from the point (1,1) to…

A: Maximum rate of change occurs in the direction of gradient vector of the function.

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 1 for time t > 0. If the…

A:

Q: Find all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, y)…

A: First find gradient and take magnitude for max rate of change

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² – 10t for time t> 0. If the…

A:

Q: Find the equation of a line tangent to the given functions at the given points of tangency. 1) f(x)…

A:

Q: The velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 · 23t,…

A: The Velocity function of the particle moving along a horizontal line is given by v(t)=ln2·23t…

Q: The height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial…

A:

Q: A particle initially situated at the origin moves along the x-axis so that its acceleration at any…

A: Integrate the expression a(t)=2t-7 to find the velocity of the particle.…

Q: Q1) Find the tangent y = vx2- x +7 at x = 2.

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

Q: At time 0<t< 2, the velocity of a particle moving along the x-axis is given by v(t)= tsin(tcubed). b…

A:

Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line

Q: A particle moves along the x-axis so that at time t>0 its velocity is given by v(t) = 6t2 - 96t.…

A: