A projectile is launched vertically from the ground at t = 0, and its velocity in flight (in m>s) is given by v1t2= 20 - 10t. Find the position, displacement, and distance traveled after t seconds, for 0 … t … 4.

Q: The velocity function (in meters per second) for a particle moving along a line is given by v(t) =…

A: Given, v(t)=t3-2t2   Interval [a,b]=[-2,3]

Q: Suppose that a particle moves along a straight line with velocity v(t) = 13 – 6t, where 0 <t < 2 (in…

A: To find the displacement at time t.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 12 4t, where 0 ≤ t ≤ 2 (in…

A: For the particle moving in a straight line  Displacement 12t-2t2 Total distance travelled is 16…

Q: If s = t2 - t³, find the velocity when the acceleration is zero. Express your answer in decimal form…

A:

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t…

A: Given:The velocity function of the particle is v(t) = 5t-8.

Q: a ball is thrown straight upwards from a tower (40 feet high) so that its position, s in feet, at…

A:

Q: The position of a particle moving along a straight line is given by s =t3-9t2+24t, where s is…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 - 8t + 17,…

A: We have solve the problem by putting the value of interval in average velocity formula.

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by = 9t3 + 4t – 18, |…

A: Given,         The displacement in meters of a particle moving in a straight line is given by…

Q: If a ball is given a push so that it has an initial velocity of 24 ft/sec down a certain inclined…

A: Here we can use the fact that the velocity is the instantaneous rate of change of distance. That…

Q: Two particles have positions at a time t given by the equations x1=t3-t and x2=6t2-t3 find the…

A: If x(t) represents position at time t then velocity = v(t) = dx/dt and acceleration = a(t) = dv/dt =…

Q: A robot moves in the positive direction along a straight line so that after  minutes its distance is…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 11 – 5t, where 0 <t 0.5 (-…

A: NOTE: Refresh your page if you can't see any equations. .

Q: A particle moving along a line has the position s(t) = t* – 1812 at time t seconds. What is the…

A:

Q: a car move with an initial velocity of * 50 m/s to the right, determine its position when t=15 s, if…

A: This is a problem related to newton's law of motion. Based on the general formula and concept we…

Q: c) Use the velocity function v(t)= 2e2m/s to compute the distance traveled by an object over the…

A:

Q: The displacement (in meters) of a particle moving in a straight line is given by s = t2 – 5t + 15,…

A: Given: s=t2-5t+15, where t is measured in seconds

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

A:

Q: 2) Find the points on the curve where the tangent is horizontal or vertical. x = t2 – 8t, y = 2t3 +…

A: A parametric equation of a curve is given by: x = t2 - 8t    and    y = 2t3 + 3t2  We have to find…

Q: Assume a particle’s position is given by f (t) = −4 / t, where t is measured in seconds and f (t) is…

A: The velocity of a particle is found by differentiating the position function of a particle,…

Q: Find the net change in velocity over [1, 4] of an object with a(t) =8t - t2 mls2 .

A: Given, Acceleration is, a(t)=8t-t2 ,ms2

Q: b) Find the point's acceleration at the specified time. s"(2) = ft/sec2 %3D

A: we have been given  s=3t-3t2   , t=2s'(t)=ddt3t-3t2s'(t)=-3t2+6t3now…

Q: A Ferrari's position at time t is given by s(t) = t3 - 9t2 + 24t 2) What is the Ferrari's velocity…

A: Given:    s(t) = t3 - 9t2 + 24 t   Velocity at t = 0

Q: Suppose an object moves along a line at 13 m/s for 0sts2 s and at 22 m/s for 2<ts5s. Sketch the…

A:

Q: (2) At what point(s) will the tangent line to y = x? - 4x +3 be horizontal

A:

Q: Find the displacement of an object on the interval 0 ≤ t ≤ 6 if its velocity is v (t) = 4t -√√t

A:

Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 – 4t, where 0 <t < 1.5…

A:

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: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

A: We will use formula for the Displacement and distance in terms of Velocity function

Q: the avrage velocity of p(t)=4.5t^2-15t+180 over[1,5]

A:

Q: Given the acceleration of an object and its initial velocity, how doyou find the velocity of the…

A: We know that the rate of change of velocity of a moving particle is known as its acceleration. Let…

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: Suppose you are standing in a field near a straight section of railroad tracks just as the…

A:

Q: Determine the velocity of the particle at t = 7.

A:

Q: Find the slope of the tangent to Ax) = x²e* at the point (1, e). a) e b) 1 c) 3e d) 2 + e

A:

Q: Suppose an object moves along a line at 19 m/s for 0sts2 s and at 25 m/s for 2<ts5 s. Sketch the…

A:

Q: If a ball is thrown vertically upward from the roof of 4848 foot building with a velocity of 6464…

A: s(t) = 48 + 64t - 16t2Hence, s’(t) = 64 – 32ts”(t) = - 32When s is maximum, s’(t) = 0; hence 64 –…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² – 10t for time t> 0. If the…

A:

Q: A particle is moving in a straight line with the velocity v(t) =1-t,0<t< 3. Compute the distance…

A: We have V=1-t⇒dxdt=1-t∫0△xdx=∫(1-t)dt

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

A:

Q: Q1) Find the tangent y = vx² – x + 7 at x = 2.

A: The detailed solution is as follows below:

Q: Consider an object moving along a line with velocity v(t) = 6t2 – 12t with t measured in seconds and…

A:

Q: A particle moving in a straight line is at a distance of s(t) = 1.lt³ + 13t feet from its starting…

A: The solution is given in next step

Q: Suppose that a turtle is moving along a straight line, and its displacement s(t) at any given time t…

A: Given data: The expression for the displacement is s(t)=(t-√(t2+3)+√3). The given interval is [a,…

Q: (a) Find the velocity of the particle at time t. s'(t) = (b) When is the velocity 0? (Use n as the…

A: Follow the procedure given below.

Q: Suppose that a particle moves along a straight line with velocity v(t) = 14 – 3t, where 0 <t< 2 (in…

A: Given, Velocity of the particle = v(t) = 14 - 3t  We have to find the displacement at time t = 2 So,…

Q: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…