The vertical position of a particle is given by the function s = t – 3t2 – 2. How far does the particle travel between t = 0 and t = 5?

Q: m Find the equation of the tang ent to the curve ym =1 at the point (x1.y1). m

A: Topic:- application of derivatives

Q: Determine the speed as a function of time t for a particle having position function r(t) (t, 10t2,…

A: We have  r(t) = <t,10t2, t4>  Speed = ||r'(t)||

Q: The displacement, in meters, of an object moving in a straight line is given by s(t) = 3+ 4t +t2,…

A: The displacement is given by

Q: The position of a particle is given by s(t) = t³ – 20.5t² – 2t, t > 0. When does the particle reach…

A: Given,           The position of a particle is given by st=t3-20.5t2-2t , t≥0.             The…

Q: The position function of a particle is given below. s(t) = t³ + 1.5t² - 55t, t z 0 When does the…

A:

Q: Find the average velocity from time t= 0 to t = 1 of a car whose position p(t) along a horizontal…

A: Here, we have, Position of car along horizontal track is pt=4-t-2 from t=0 to 1 It is known that…

Q: The driver of a car traveling at 48 ft/sec suddenly applies the brakes. The position function of the…

A: Topic- application of derivatives

Q: 4. The position of an fictitious particle moving in a straight line, in metres, is described by the…

A:

Q: The position function of a particle is given below. s(t) = t3 + 6t2 − 59t, t ≥ 0 When does the…

A: Given,         The position function of a particle is given below :          st=t3+6t2-59t ,t≥0…

Q: (b) Find the value of k for which 2y +x k is a tangent to the curve y +4x 20. %3D

A:

Q: A weather balloon is released and rises vertically such that its distance s(t) above the ground…

A: s(t)= 6+13t+8t^2 ds/dt = v = 13+16t v= 13+ 16(52) v= 13 + 832 v= 845.

Q: A particle is moving along a horizontal line such that its velocity is given by v(t) = 3ť² – 24t+36,…

A: Let's find.

Q: Q4) find at t= from the following functions, x= cost . y= 1+sint

A: Given that  x=cost  y=1+sint  To find the d^2y/dx^2 at t=π/2

Q: The position function of a particle is given below. 6t2 91t, t 2 0 s(t) t3 When does the particle…

A: To determine the time when the particle reach a velocity of 5 m/s.

Q: A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 .…

A:

Q: A rock is thrown vertically upward with a velocity of 256 ft/s, so its position function can be…

A: A rock is thrown vertically upward with a velocity of 256 ft/s, Its position function can be modeled…

Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

A: Solve

Q: The position of the particle at time t is given by s(t) = t² – 18t + 80. %3D The particle is moving…

A: The particle will move from left to right if the velocity is positive

Q: The position function of an object is given by s(t) = -t + 2t. For t > 0 and s(t) = 0m, the velocity…

A:

Q: The position function of a particle is given by s(t) = t-1.5t2-2t for tz0. At what value of t does…

A: To find the velocity function , then at which time velocity will be 166 m/sec.

Q: The position of the particle at time t is given by s(t) = t² – 8t + 15. %3D The particle is moving…

A: Concept used particle will move fromleft to right when velocitydvdtbecome positive.dsdt>0

Q: For a t-curve with df = 11, find the t-value to 10: O A. 1.280 ОВ. 1.363 O C. 2.718 O D. 1.372

A: Given Degrees of freedom (df)=11

Q: given the position function for an object in motion is s(t)=2t2+4t-1 what is the average velocity on…

A: Definition used:The average velocity of an object with position function f(t) over an interval [a,…

Q: For a given table 2 4 6. 8 y 9. 16 23 d'y Find the value of at x = 4 using forward difference…

A:

Q: (a)Differentiate t + 3t* – 2t with respect to t. (b) 4 (x³ – - * +) with respect to x. (c) Find when…

A:

Q: The position of an object moving along a line at any time t > 0 is given by the function s(t) = t3 –…

A:

Q: The position function of a particle is given bys = t3 -4.5t2 -7t         t≥0(a) When does the…

A: Given the position function of a particle is s=t3-4.5t2-7t, where t≥0. (a). We know that velocity of…

Q: The position function of a particle is given below. s(t) = 3 + 6t2 - 61t, t > 0 When does the…

A: Velocity function is the derivative of the position function. So differentiating s(t) with respect…

Q: The value of b makes the line y = 2x +b be tangent to the function f (x) = x² is O -1 none О 1 O 2

A: Tangent line related problem......

Q: dt F(x) = | 6+ 8t Find the interval on which the curve is concave downward.

A:

Q: For a t-curve with df = 20, find the t-value to.01- O A. 1.325 O B. 2.528 O C. 2.330 O D. 2.539

A:

Q: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t> 0,

A:

Q: The position function of a particle moving along the x−axis is given by x(t)=t3−4t2+5t−2, t≥0. Find…

A: We find the velocity by finding the first derivative of x(t)

Q: The position function of a particle is given below. s(t) = t3 + 1.5t2 - 16t, t 0 When does the…

A:

Q: The position function of a golf ball rolling on an incline is given by d(t) = 4r² + 7t, where d is…

A: position function of the rolling golf ball is given. It is asked to find velocity of golf ball at…

Q: For a t-curve with df = 11, find the t-value to 10: O A. 1.280 В. 2.718 O C. 1.363 O D. 1.372

A:

Q: A ball rolls down an inclined plane such that the distance (in centimeters) that it rolls in t…

A: Differentiate the function s(t)=2t3+3t2+4 to find the velocity function.…

Q: The position function of a particle is given below. s(t) = t3 + 1.5t2 - 55t, tz 0 %3D When does the…

A:

Q: Q4) find at t= from the following functions, x= cost. y= 1+sint

A:

Q: The position function of a particle is given by = t3 – 10.5t2 – 2t, t > 0 When does the particle…

A:

Q: The position function of a particle is given by s(t)=t^3−4t^2−8t, t≥0 where s is measured in meters…

A: To find the velocity function from the position function, we have to differentiate position function…

Q: The velocity of an object moving along a line is given in the graph below for 0 <t < 8. Att = 0, the…

A:

Q: The position function of a particle is given below. s(t) = t3 + 3t2 - 6t, t 2 0 When does the…

A: The velocity function of a particle is given byv(t)=ddts(t)

Q: If y1=2x+4 and y2 =x^2+C, find the value of C such that y2 is tangent to y1

A: Given: y1=2x+4    and    y2 =x²+C   To find :the value of C such that y2 is tangent to y1

Q: Find the length L of the curve R(t) = 4ť²i + t° j+ 4k over the interval [3, 6]. L

A:

Q: The position of a particle is described by the function f (t) = t³ – 3t? + 8t + 1. Consider the…

A: givenposition of a particlef(t)=13t3-3t2+8t+1the distance travelled by the particle between t=0 and…

Q: find the velocity at 2 seconds for the position function s(t) =-16t2+35t+55 where distances are…

A:

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A:

Q: The velocity on [4,6] can be modeled by the function v,(t) = 5t³ – 75t² + 360t – 550. %3D 49) Write…

A: The velocity function is v7(t)=5t3-75t2+360t-550

Q: The displacement of a particle moving back and forth along a straight line is given by the motion…

A: We have to solve given problem: