Let s(t) = 5t2 – 22t be the position function of a particle moving along a straight line, where s is in feet and t is in seconds. When, during the time interval 1

Q: Find the derivative dydx for the function x=1t+t, y=1t2 at the point t=12.

A: Here given

Q: A particle moves with position function s(t) = t – 4t³-20t?+20t where t > 0. At what time does the…

A: This question is based on application of Derivative.

Q: A proton moves in an electric field such that its acceleration (in cm s-²) is given by: 40 a(t) (4t+…

A:

Q: A particle moves along the x-axis so that at timet >0 its position is given by x(t) = 3t3 - 9t? –…

A: Given that x(t)=3t3-9t2-72t. We need to determine all the intervals when the acceleration of the…

Q: The movement of a particle from time t=0 to t=9 is given by the equation s(t)=−5t2−5t−10. What is…

A:

Q: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocityis…

A:

Q: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s2 ? =…

A: To find: The instantaneous velocity at t=2. Given: The acceleration of particle is a=12t2-24t+8.…

Q: An object with an initial velocity of v(0) = 5 has an acceleration of a(t) = t² - 5. What is its…

A: Concept: The acceleration is given by the derivative of the velocity  That is a(t)=dv(t)dt Thus…

Q: If the position of an object is s(t) = 16 + 10.5t – 4.9t meters from zero in t seconds, then what is…

A:

Q: A particle moves with position function s = t4 – 4t3 20t2 + 20t, t > 0 - (a) At what time does the…

A: Given problem:- A particle moves with position function   S=t4 -4t³ - 20t² + 20t, t≥ 0   (a) At what…

Q: A particle moving along the x-axis has position function p(t)=−t^3+t^2+2t+1. Find the acceleration…

A:

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: a particle moves according to the function s(t)= t^2 - 2t +5,  what is the instantaneous velocity of…

A: A particle moves according to the function s(t)=t2-2t+5

Q: Let s(t) = 5t2 - 22t be the position function of a particle moving along a straight line, where s is…

A:

Q: Find velocity (f'(x)) and acceleration (f''(x)) at time or t=0 with equation s(t)=2((e^t)-(e^-t))

A: We have to find velocity and acceleration

Q: A particle moves along the x-axis with an acceleration given by a(t) = 7t + 8, where t is measured…

A:

Q: The value of the instantaneous velocity at t = 1 is

A: Consider the position function To calculate the instantaneous velocity

Q: Q2. A particle moves along a straight line so that aftert (seconds), its distance from Oa fixed…

A:

Q: ) Suppose that the acceleration function of a particle moving along a coordinate line is a(t) = t –…

A: a)Givena(t) = t - 3Now average acceleration is given by ∫aba(t)dtb-aHere a=0 and…

Q: The acceleration of a particle moving along a horizontal line is given by a(t) = 2t - 2. If particle…

A:

Q: A particle moving along a line has position s(t) = t 4 - 18t2 m at time t seconds. At which times…

A: st=t4-18t2 Substitute 0 for s(t) into above position function. st=0t4-18t2=0t2t2-18=0t=0 or t2=18t=0…

Q: At time t=0, a driver jumps from a diving board that is 25 feet high. Because the drivers initial…

A: Given, Position function, h(t) = -16t2+15t+25 a) When the diver hit the water, h(t)=0…

Q: 3. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A: Consider the given position function. st=-t3+3t2-6 Find the double derivative of the position vector…

Q: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s^2 is…

A:

Q: Show that for motion in a straight line with constant acceleration a, initial velocity v0, and…

A: Let the acceleration a(t) = a, constant.Take integral on both sides to get velocity equation,

Q: Suppose the function p(t)=(t^2 - 2)e^2t represents the position of a particle at time t. Determine…

A:

Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t - 3 mis over…

A: Given velocity of particle is vt=4t-3. To find the dispalcement of particle over time interval 2,5.…

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

A: Given: The velocity of the particle along x-axis is vt=10t+12 The particle is at the position x=2 at…

Q: A particle moves along a straight horizontal line so that its position at any time is given by s(t)…

A: Let's find.

Q: The movement of a particle from time t=0 to t=4 is given by the equation s(t)=−5t2−10t−6. What is…

A:

Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 16t3 – 12t, - then the…

A: We will find out the required value.

Q: 7. A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s²…

A: Given a particle starts from rest and moving along straight line has acceleration a is given as:…

Q: A particle moves along the x axis with position measured relative to the origin and has an…

A: Consider that acceleration of object is given by at=6t+4 cm/s2, initial velocity is -6 cm/s and…

Q: 3. The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t° – 15t –…

A: Velocity and acceleration from displacement function of time t

Q: A train moves at a velocity of v(t)= 3t" - 3200t km/sec where t in seconds is the time passed since…

A: Find your answer below

Q: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 12t – 6 for timet > 0. If the…

A:

Q: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

A:

Q: A Ferrari's position at time t is given by s(t) = t3-9t2 + 24t 4) At what time is the acceleration…

A: Given the equation of position of Ferrari's s(t)=t3−9t2+24t    ....(1)

Q: An object moving in a straight line has an acceleration in m/s2 given by a = 18t + 4. Find its…

A:

Q: A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times…

A: St=t4-18t2The particle passes through the origin when St=0t4-18t2=0t2t2-18=0t2=0   t2-18=0⇒t=0…

Q: A particle's position with respect to time as it moves along a coordinate axis is given by the…

A: Given position function,p(t) = t3+3t2+3t+1

Q: If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 80…

A: We need to find height, velocity, acceleration.

Q: For time t > 0, a particle moves along the x-axis, its position is given by the function s(t) = -t3…

A: Given: s(t)=-t3+3t2-6 For a given position function s(t) , velocity and acceleration is defined as…

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

A:

Q: Q2. A particle moves along a straight line so that after t (seconds), its distance from Oa S = t³ –…

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…

Q: An object is moving along a straight line with its position in feet at time t in seconds given by s…

A: Given, Displacement of body s(t)=t3-2t2-7t+9

Q: A particle moves in a straight line with velocity v(t)=t2 How far does the particle move between…

A:

Q: The position of a body moving along s-axis at any time 't is given by s(t) = 4t- 12t, then the…

A: