Bike race Theo and Sasha start at the same place on a straight road, riding bikes with the following velocities (measured in mi/hr). Assume t is measured in hours. Theo: v7(t) = 10, for t = 0 Sasha: vs(t) = 15t, for 0 s t s 1 and v3(1) = 15, for t > 1 %3D a. Graph the velocity functions for both riders. b. If the riders ride for 1 hr, who rides farther? Interpret your answer geometrically using the graphs of part (a). c. If the riders ride for 2 hr, who rides farther? Interpret your answer geometrically using the graphs of part (a).

Q: At time t, the position of a body moving alongthe s-axis is s = t3 - 6t2 + 9t m. Find the body’s…

A: We find v and a using the first and second derivative of s. We use the power rule.

Q: Consider the accelertation function of a particle a(t)= -cost + 2e^t measured in meters per…

A: Let a(t) be the acceleration function of a particle at time t. Then velocity function of this…

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: ds The position of a particle at time t is given by s. Find the velocity dt 4 - 5st + 2t - 7t= 0

A:

Q: A particle moves in a straight line with the given velocity v(t) = 4t-2 – 1 (in m/s). Find the…

A:

Q: Theo and Sasha start at the same place on a straight road riding bikes with the following velocities…

A: (a) The velocity of Theo is vTt=10 for t≥0. Note that the velocity function dos not depend on the…

Q: Find the position function if a velocity function is given by v(t) = 21 e -2t. %3D s(t) = %3D (Type…

A: Integration of velocity function is position function.

Q: Suppose the position of an object moving in a straight line is given by s(t)= 3t - 7t-8. Find the…

A:

Q: Suppose the position function for a free-falling object on a certain planet is given by s(t) = -11t5…

A:

Q: Suppose the position (in s(t) = -2t2 + 12t for 0 s %3D a). Find the velocity fu stationary, moving…

A: A) s(t) =-2 t2 + 12tv(t) =dsdt = ddt(-2 t2 + 12t)v(t) = -4 t +12   When the object is stationary,…

Q: The position function of a particle is given by s(t) =3t-t, t20. (e) When does the particle reach a…

A: Topic- application of derivatives

Q: A ball having mass m falls from a tower with heigh h from the ground. The velocity of the ball…

A: The velocity of the ball satisfies the relation, mdvdt = -mgat t = 0  velocity v = 0 given relation…

Q: At time t Ú 0, the velocity of a body movingalong the horizontal s-axis is y = t2 - 4t + 3.a. Find…

A: Given, v(t)=t2-4t+3 a)The body’s acceleration each time the velocity is zero v(t)=0…

Q: 21. A particle follows the trajectory x(t) 4 t3 +2t, y(t) = 201 – 12 with t in seconds and distance…

A: The trajectory of particle is given as

Q: Q8: If L = 100, h = 6, and v0 = 450mph, sketch a graph of dy/dt. What does this tell us about…

A: Given:y(x) = 2hL3x3 + 3hL2x2   (miles)                       (1)v0     = dxdt      (mph)…

Q: A particle is moving along a straight line such that when it is at the origin it has a velocity vo.…

A:

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

A: The object is at rest when the velocity is zero. X- axis : time Y-axis: velocity

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

A: Velocity time graph given in the figure.  Initial position=10 Find the position after t=5 And total…

Q: Beginning at t = 0 with initial velocity 7 m/s, a particle moves in a straight line with…

A:

Q: Suppose the position of an object moving in a straight line is given by s(t) = t2 + 5t + 2. Find the…

A: we have to find the instantaneous velocity at t=1 position of the object is ,  s(t)=t2+5t+2

Q: Suppose the position function for a free-falling object on a certain planet is given by s(t)= – 131+…

A: In this we have to find out the derivative of position function so that we can get velocity so I'm…

Q: Suppose the position of an object moving in a straight line is given by the specified function. Find…

A:

Q: ; For the distance time graph given, a) sketch the velocity and acceleration function. Ef 3 5 b)…

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

A:

Q: A particle moves in a straight line with acceleration a(t) = 3t2 + et, initial velocity v(0) = 4

A:

Q: ds The position of a particle at time t is given by s. Find the velocity dt s4-7st+2t-3t= 0 ds dt

A:

Q: (a) Suppose the distance s (in feet) covered moving along a o ha Straight ine road after t seconds…

A:

Q: s = -t² + 6t –1 and 0<t <1 then the velocity at t = 1 is

A:

Q: Suppose the position of an object moving in a straight line is given by the specified function. Find…

A:

Q: Suppose position function of (t)=t^3-10.5t^2+30        0≤t≤6 1) whats the velocity of the function?…

A:

Q: At time t, the position of a body moving alongthe s-axis is s = t3 - 6t2 + 9t m. Find the body’s…

A:

Q: At time t, the position of a body moving alongthe s-axis is s = t3 - 6t2 + 9t m. Find the total…

A:

Q: A bead slides down the curve xy = 10. Find the bead’s horizontal velocity at time t = 2 s if its…

A:

Q: he velocity v(t) in the table above is decreasing, 2 raveled, find O An upper estimate = units

A: Here we have,

Q: The table gives the position s1t2 of an objectmoving along a line at time t, over a two-second…

A:

Q: (a) Find the acceleration at time t = 5 min of a helicopter whose height is s(t) = 300t − 4t3 m.(b)…

A:

Q: An object moves on a horizontal coordinate line. Its directed distance s from the origin at the end…

A: Please find attachment for the details solution

Q: A particle moves along a vertical coordinate axis so that its position at any time between 0 and 10…

A:

Q: Given a particle moving according to s(t) = %3D t2 +9 (A) Find the velocity function. (B) What is…

A:

Q: 1. A particle starts from rest and has an acceleration function, a(t) = 9-24t m/s?. a) What is the…

A: Velocity

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

A:

Q: In winter, cold wind blows from North to South which brings dramatic decrease in temper- atures in…

A: According to the given data in question you try to solve this problem

Q: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 13 for time t > 0. If the…

A:

Q: B. The position of a particle moving along a horizontal line is given by r(t) = t-6t²+9t, where t20…

A: given x(t)=t^3-6t^2+9t

Q: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

A:

Q: At time t&gt;=0, the velocity of a body moving along the horizontal s-axis is        y = t2 - 4t +…

A: Given,

Q: A particle moves along the curve (t)=⟨2t/1+t2,1−t2/1+t2⟩. Find the speed of the particle at t=1.

A: Given position vector is,

Q: A particle in R2 has a velocity function of v(t) = (3t²-4, 6t + 2) (given in m/s). After moving for…

A:

Q: Q1. A particle moves along a straight line so that after t (seconds), its distance from O a fixed…

A: A particle is moving along the straight line so that it's distance from a fixed point 'O' after time…