= etî + etj + V2tk; 0 < t < In 3, then r = the displacement and the distance traveled over the indicated time interval :is 7 3
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E Expert Q&A
r = e'î + etj+ V2tk; 0 < t < In 3, then
the displacement and the distance
traveled over the indicated time interval
:is
Let
C : r(t) = tî + t³/2} ((0 < t < 3),
1
ds
x + 1
= then
5 O
3о
1 0
4 0
2 0
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- An object's position as a function of time in one dimension is given by the expression; 3.89t2 + 2.22t + 7.48 where are constants have proper SI Units. What is the object's average velocity between the times t = 3.16 s and t = 8.38 s?Nerve impulses in a human body travel at a speed of about 100 m/s. Suppose a person accidentally steps barefoot on a pebble. About how much time does it take the nerve impulse to travel from the foot to the brain (in s)? Assume the person is 1.60 m tall and the nerve impulse travels at uniform speed.An equation describing displacement (in meters) as a function of time (in seconds) of a rocket propelled motorcycle moving up a hill is given by: x(t) = 13.5t – 0.5t³ + 7 Where 0Andrew has several tables filled with data describing moving objects. Which table has data thatdescribes an accelerating object?A race car moves such that its position fits the relationship x-(4.5 m/s)t + (0.80 m/s³³ where x is measured in meters and in seconds. (a) A plot of the car's position versus time is which of the following? برسا 100- O x(m) 90 80 70 60 30 30 20 10 O x(m) 240 220 200 180 160 140 1201 100 80 60 200 180 160 140 120 EL 100 80 40 20 t(s) 40 1.00 2.00 20 t(s) 3.00 4.00 5.00 6.00 1.00 2.00 3.00 4.00 5.00 x(m) 6.00 30 25 20 15 10 5 x(m) t(s) 1.00 2.00 3.00 4.00 5.00 6.00 220 t(s) 1.00 2.00 3.00 4.00 5.00 6.00 (b) Determine the instantaneous velocity of the car at t-4.4 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (In order to better see the limiting process keep at least three decimal places in your answer.) At-0.40 s m/s (Use the interval from t-4.20 sto 4.60 s.) At -0.20 s m/s (Use the interval from t-4.30 sto 4.50 s.) At - 0.10 s m/s (Use the interval from t-4.35 sto 4.45 s.) (c) Compare the average velocity during the first 4.4 s with the results of part (b). The average velocity…Here are a couple acceleration problems. Acceleration isn't necessarily constant. These problems will be pure math problems, meaning that we won't use units. a(t) = dv/dt = 146 cos(4t) v(t) = dx/dt, v(0) = -3, and x(0) = -6 Calculate x(6).Two-dimensional motion: Object A has a position as a function of time given by rA(t) = (3.00 m/s)t i + (1.00 m/s2)t2j. Object B has a position as a function of time given by r p(t) = (4.00 m/s)ti + (-1.00 m/s2)t2i. All quantities are SI units. What is the distance between object A and object B at timet= 3.00 s?A velocity vs. time graph is shown below. Which acceleration vs. time graph cor- responds to the velocity vs. time graph? Velocity m T -10+ + -15+ A D 2 4 Aggeleration R 2 4 6 8 10 Time (x) -00 00 Agceleration Time() 2 4 6 8 10 + 6 + 8 10 Time (s) Aggeleration. F 2 4 6 8 10 Time (s) с R 2. 6810The speed of an object as a function of time is given by the following equation: What is the magnitude of the object's acceleration (in m/s2) at t = 5 s? X 32The x component of the velocity of an object moving along the x axis is given as vy = 4t – 3t where vy is in meters per sec and t in seconds. The x component of its average velocity over the interval of time from t =0 to t= 2 sec is: O -2m/s O 2 m/s O -4m/sv(t) = 4t3 + 10t m/s. The initial position is r = 3 m. 3. A one dimensional problem. Assume v = Determine the position and acceleration at time t = 3sec.A remotely controlled toy car travels along a straight line and its position changes with time following the law: x(t)=51³-1²+1 where time t is measured in seconds and the coefficients have such dimensions that the position x(t) is measured in meters. 10. What is the displacement of the car for the first 2 seconds since the start at t=0 s? 11. What is the average velocity of the car for the time period between the t=0s and t=2 s? 12. What is the instantaneous velocity of the cat at t=2s ? 13. What is the instantaneous acceleration of the car at t=2 s?