Finding Tangential and Normal Components of Acceleration In Exercises 25-30, find the tangential and normal components of acceleration at the given time tfor the plane curve r( t).
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Calculus: Early Transcendental Functions
- Represent the plane curve by a vector-valued function. y = x+ 1 r(t) = ti + (t+1)j Need Help? Read Itarrow_forwardSketch the curve represented by the vector-valued function r(t) = 2 cos ti + tj + 2 sin tk and give the orientation of the curve.arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 4 cos ti + 4 sin t (2V2,2V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the objeot. v(t) s(t) = a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point.arrow_forward
- Sketch and describe the curve defined by the vector-valued function below. 7(t) = (t cos t, t, t sin t), t > 0. Explain, in words, some properties of the curve as t gets bigger.arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given point. (c) Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point. Position Vector r(t) = ⟨e−t, et⟩ Point (1, 1)arrow_forwardRepresent the plane curve by a vector-valued function. y = x + 1 r(t) = (t)i+ (t 1)j %3Darrow_forward
- The concentration of salt in a fluid at is given by mg/cm . You are at the point . (a) In which direction should you move if you want the concentration to increase the fastest? Direction: (Give your answer as a vector.) (b) You start to move in the direction you found in part (a) at a speed of cm/sec. How fast is the concentration changing? Rate of change = HINT: The rate of change of the perceived concentration F(x,y,z), by the Chain Rule, equals the dot product of the gradient vector of F and the velocity of the "particle". To find it, we need to know the norms (magnitudes) of both vectors and the angle between them. In this problem the angle is known.arrow_forwardRepresent the plane curve by a vector-valued function. y3x + 1 r(t) Need Help? Read Itarrow_forwardRepresent the plane curve by a vector-valued function. y = (x − 2)2arrow_forward
- Determine the domain of the vector function r(t) = cos(4t) i + 7In(t - 5) j - 10 k Evaluate if the vector function is possible at the value of t=8, round to two tenths Find the derivative of the vector function r(t)arrow_forwardThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3/2, 3/2) %3D (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = %3D s(t) = %3D a(t) = %3D (b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D al %3D IIarrow_forwardCalculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t) , sin(t)) when t Velocity: Acceleration: Speed: Usage: To enter a vector, for example (x, y, z), type ""arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage