Question

In: Math

The displacement (in meters) of a particle moving in a straight line is given by s...

The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 4t + 16, where t is measured in seconds.
(a) Find the average velocity over each time interval.
(i) [3, 4]


(ii) [3.5, 4]


(iii) [4, 5]


(iv) [4, 4.5]


Solutions

Expert Solution

We find out the average velocity of given function over the given time interval.


Related Solutions

The displacement (in centimeters) of a particle moving back and forth along a straight line is...
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 3 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i)    [1, 2] _______cm/s (ii)    [1, 1.1] _______ cm/s (iii)    [1, 1.01] ______ cm/s (iv)    [1, 1.001] _______cm/s B) Estimate the instantaneous velocity of the particle when t=1.
The position of a particle moving along a line (measured in meters) is s(t) where t...
The position of a particle moving along a line (measured in meters) is s(t) where t is measured in seconds. Answer all parts, include units in your answers. s(t)=2t^3 +6t^2 −48t+7 −10<t<10 (a) Find the velocity function. (b) Find all times at which the particle is at rest. (c) On what interval is the particle moving to the right? (d) Is the particle slowing down or speeding up at t = −1 seconds?
The velocity function for a particle moving along a straight line is given by v(t) =...
The velocity function for a particle moving along a straight line is given by v(t) = 2 − 0.3t for 0 ≤ t ≤ 10, where t is in seconds and v in meters/second. The particle starts at the origin. (a) Find the position and acceleration functions for this particle. (b) After ten seconds, how far is the particle from its starting point? (c) What is the total distance travelled by the particle in the interval [0, 10]?
Suppose a particle is moving right and left in a straight line. Its position, in centimeters,...
Suppose a particle is moving right and left in a straight line. Its position, in centimeters, at time t seconds is given by the function s(t) = −t3 + 12t2 − 21t. (For the purposes of this problem, assume that t ≥ 0.) (a) At what t-values is the particle stopped (that is, has a velocity of zero)? (b) Over what time interval(s) is the particle moving left? (c) Find the acceleration of the object when t = 4.
Suppose a particle is moving right and left in a straight line. Its position, in centimeters,...
Suppose a particle is moving right and left in a straight line. Its position, in centimeters, at time t seconds is given by the function s(t) = −t^3+ 12t^2 − 21t. (For the purposes of this problem, assume that t ≥ 0.) (a) At what t-values is the particle stopped (that is, has a velocity of zero)? (b) Over what time interval(s) is the particle moving left? c) Find the acceleration of the object when t = 4.
1. The position of a particle moving in a straight line during a 5–second trip is...
1. The position of a particle moving in a straight line during a 5–second trip is s(t) = 2t2 − 2t + 2 cm. Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip beginning at t = 0. 2. a) A particle moving along a line has position s(t) = t4 − 34t2 m at time t seconds. At which non negative times does the particle pass through the origin?...
The position function of an object moving along a straight line is given by the function...
The position function of an object moving along a straight line is given by the function t3 - 15t2 -48t -10, where s is in metres and t is in seconds and 0≤15≤t . [7A] a) When is the velocity of the object greater than 21 m/s? b) When is the speed of the object less than 21 m/s? c) Illustrate the graphical representation for each of the above."
a particle moves aling a straight line and its position at time t is given by...
a particle moves aling a straight line and its position at time t is given by s(t)= (t^3)-13.5t^2+54t where s is measured in feet and t is seconds. consider t in the interval [0,infinity) 1) when is the particle moving in the positive direction? ( i tried (0,3) U(6, infinity) but it didnt work) 2) what is the total distance the particle travels travels between time 0 and time 7 3) when is the particle speeding up? 4) when is...
The velocity function of a particle moving along a line is given by the equation v(t)...
The velocity function of a particle moving along a line is given by the equation v(t) = t2 - 2t -3. The particle has initial position s(0) = 4. a. Find the displacement function b. Find the displacement traveled between t = 2 and t = 4 c. Find when the particle is moving forwards and when it moves backwards d. Find the total distance traveled between t = 2 and t = 4 e. Find the acceleration function, and...
1) The position of an object moving along a straight line is s(t) = t^3 −...
1) The position of an object moving along a straight line is s(t) = t^3 − 15t^2 + 72t feet after t seconds. Find the object's velocity and acceleration after 9 seconds. 2) Given the function f (x ) =−3 x 2 + x − 8 , (a) Find the equation of the line tangent to f(x ) at the point (2, −2) . (b) Find the equation of the line normal to f(x ) at the point (2, −2)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT