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1. If the velocity of a particle is given by v(t) = 4t + 4 and s(l) = 2, find the particular position function s(t). 2. Find f(x) if f'(x) = and f(2)= 0. 3. Find the sum of the areas of approximating rectangles for the area under f(x) = 48 – x?, between x = 1 and x = 5 using 4 subintervals and the right endpoints of each subinterval for sample points. 4. If S* f(x)dx =...
10. The velocity function of a particle is given by v(t) = 2t - 4 on the interval (0,4), where t is measured in seconds, and velocity is measured in meter per second. Sketch the graph of the velocity function, determine the displacement over the given interval and find the total distance traveled by the particle over the given interval.
Int The velocity of a particle along a path is given by v(t)= fort > 0.6 points each) a. Find the acceleration function of the particle along this path. t b. Find the position function of the particle given that its position at t=1 is 5.
The velocity of a particle moving in a straight line is given by v(t) = 2 + 2. (a) Find an expression for the position s after a time t. s(t) = + C (b) Given that s = 3 at time t = 0, find the constant of integration C. C = 1 Find an expression for s in terms of t without any unknown constants. HINT [See Example 7.]
The acceleration of particle is given as a function of velocity, a(v), find the position as a function of velocity, v(s)
v=(4 + + 2) m/s 1. The particle is moving with a velocity of v = (4 + 2) m/s, where t is in seconds. When t = 1 s, determine: (1) the magnitude of velocity, (2) the magnitude of acceleration, and (3) the position of the particle. (15 points) va (4+²+2) t= ls racom 6 m
For t ≥ 0, a particle moves along the x-axis. The velocity of the particle at time t is given by v(t)=1+2sin(t^2/2). The particle is at x=2 at time t=4. a)Find position of particle at t=0 b)Find the total distance the particle travels from time t=0 to time t=3
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the particle at time t 4. b) Find all times t in the open interval 0<t <5 at which the particle changes direction. During which time intervals, for 0st s 5, does the particle travel to the left? c) Find...
1095 (1999AB, Calculator). A particle moves along the y-axis with velocity given by v(t) = t sin(t?) for t 0. a) In which direction (up or down) is the particle moving at time t = 1.5? Why? b) Find the acceleration of the particle at time t = 1.5. Is the velocity of the particle increasing at t = 1.5? c) Given that y(t) is the position of the particle at time t and that y(0) = 3, find y(2)....
A particle moves with position given by s(t) = t 1 with t > 0. + where s is in meters and t is in seconds (a) Find the velocity function u(t). (b) Find v(2). Include units in your answer. (c) Find the acceleration function a(t). (d) When is the particle at rest? (You only need to consider t 0.) (e) Find the total distance traveled by the particle on 0 STS 3.