The displacement, in meters, of an object moving in a straight line is given by s(t) = 3+ 4t +t2, wheret is measured in seconds. Find the instantaneous velocity when t 3.

Q: Suppose the position of an object moving in a straight line is given by s(t) = 4t + 3t+ 4. Find the…

A:

Q: Suppose the position of an object moving in a straight line is given by s(t)= 5t + 3t + 4.. Find the…

A: We can find the answer as below.

Q: A particle moves on a vertical line so that its coordinate at time t is y = t – 12t + 3, t 2 0,…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: If a ball is thrown into the air with a velocity of 34 ft/s, its height (in feet) after t seconds is…

A:

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: Suppose the position of an object moving in a straight line is given by s(t)= 5t2 − 2t − 7. Find the…

A: The position function of an object moving in a straight line is given by st=5t2-2t-7 The…

Q: Find the velocity of a particle when  S = t2 + 3t - 4 at t = 1 sec

A:

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

A:

Q: When d is in feet, t in second , find the velocity at t= 2 of the motion s = t^2 +3t

A: s=t2+3tVelocity of the particle isdsdt=2t+3On putting the value oft=2

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: 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: Suppose the height of a rocket rising vertically from the ground is modelled by the equation; S(t)=…

A: Here equation is S(t)=t2+2t+4A)we have S(t)=t2+2t+4put t=1 and t=8 in…

Q: For f(t) = (2x − 3)3, find the equation of the tangent line at (a)  x = 0 (b)  x = 2

A: We have to find tangent line to f(x) at two different points, f(x) is given .at x=2 y=1at x=0 y=-27

Q: Use the graph of position, h(t), shown to estimate the velocity, v(t), at t = 1s. Time (sec) in (w)…

A:

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

A: Consider the position function To calculate the instantaneous velocity

Q: t 2 If the velocity of a moving object is y(t) = --- 2 12 in meters per second, then what is its…

A: The veloctiy of a moving objcet is v(t)=t2-2t2 in meters per second.

Q: Suppose the position of an object moving in a straight line is given by s(t) = 5t2 − 2t − 7. Find…

A: Given: s(t)=5t2-2t-7, at t=2

Q: Find an equation of the line tangent to the following curve at the point (a,f(a)). f(x) = 8 ex + 5x;…

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 velocity of a particle moving along a straight line is given by v(t) = 6t² + 4t – 5 cm/sec at…

A:

Q: Show that for an object falling according to Galileo’s formula, the average velocity over any time…

A:

Q: With time t in seconds, the velocity of a bicycle, in feet per second, is given by At) = 4t. How far…

A:

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: 9. The velocity, in kilometers per hour, of a car as it beings to slow down is given by the equation…

A:

Q: Suppose the position of an object moving in a straight line is given by s(t)= 5t2 − 2t − 7. Find the…

A: Given position of an object moving in a straight line is given by: st=5t2-2t-7 To find the…

Q: A particle moves on a vertical line so that its coordinate at time t is y = t³ – 12t + 3,t > 0,…

A: Speeding up and slowing down is depend on the acceleration of particles so first find the…

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: The position (in metres ) of an object moving in a straight line is given by s(t) = t° + 2t – 5, The…

A: To find the instantaneous velocity at t=1.5 seconds

Q: The position function of a particle is given by s(t) = 3t2 – t3, t > 0. (a) When does the particle…

A: The given position function is:  s(t)=3t2-t3So, the velocity function…

Q: s =t² – 7t +15, where t is measured in seconds. (A) (i) Find the average velocity over the time…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: A particle is moving along a straight line so that v ft/sec is the velocity of the particle at t…

A: Given v=t+3t2+3t+2. The objective is to find the distance traveled by the particle from the time…

Q: nen does the particle reach a velocity of 137 m/s if its position function is given by:…

A:

Q: On Earth, in the absence of air friction, a rock thrown vertically upward at a velocity of 64 feet…

A:

Q: Find the derivative of the function. s(t) = 44 (8t° -5) %3D s'(1) =D 65

A: st=448t3-565

Q: The distance of a body travels as a function of time and is defined by x(t) = 18t + 9t^2. What is…

A: Given that: Distance travelled by the body is given by:             x(t)=18t+9t2

Q: Suppose the position of an object moving in a straight line is given by s(t) = 7t³ -² +6. Find the…

A:

Q: Suppose the position of an object moving in a straight line is given by s(t) = 5t2 − 2t − 7. Find…

A: Given: s(t) = 5t2 − 2t − 7

Q: The position of a moving object is given by the function s (t) = 4t² – 10. What is the instantaneous…

A:

Q: If a rock is thrown into the air on small planet with a velocity of 30 m/s, its height (in meters)…

A: Given;  y=30t-4.9t2

Q: Find the velocity and acceleration when t = 3. %3D X =t° -3t –5

A: Solution is given as below:

Q: For 0<b<90 minutes, explain the meaning of | R(t)dt in terms of fuel consumption for the plane.

A: Explain the meaning of the given integral.

Q: At time t20, the velocity of a body moving along the s-axis is v=² - 7t+6. When is the body's…

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: The velocity (in feet per second)of a partice moving along a line is v(t) = t – 10t² +29t – 20 -…

A:

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

A:

Q: Given the position function s(t) = 12t – 5t? find the velocity and acceleration using the definition…

A:

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

A:

Q: Find a general expression for the velocity of the rock at any time t. s(t)=64-16t2,

A: Given,The displacement vector of a rock, S(t) = 64 – 16t2We need to find the general expression of…

Q: If a ball is thrown into the air with a velocity of 40ft/s, its height (in feet) after t seconds is…

A: Consider the given question,The distance(y) equation is given as,

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: