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The velocity of a particle moving in a straight line is given by v(t) = 2...
The velocity of a particle moving along a straight line is given by v = 0.2s1/2 m/s where the position s is in meters. At t = 0 the particle has a velocity v0 = 3 m/s. Determine the time when the particle’s velocity reaches 15 m/s and the corresponding acceleration. Ans: 600 s, a = 0.02 m/s2
2. (8 points) Suppose a particle is moving in a straight line with velocity v(t) = (x + 1)2 – 2 meters per second, with an initial position s(0) = 8 meters. Find the total distance traveled by the particle after 9 seconds. Round to the nearest hundredth.
1. The acceleration of a particle moving in a straight line is given by a = ut+1. The particle starts out at t=0 s with a position of r=0 m and a velocity of 2.0 m/s. Find its velocity after 5 s.
2. The velocity of a particle moving along a horizontal line is given by v(t) = sin(t). Find the distance travelled by the particle from time t = 0 to t = 21. A. 0 B. 1 C. 2 D. 4 E. None of the above. 6. When you increase the side of a cube by 2%, by what percentage does the volume approximately increase? A % B.2% C.4% D. 6% E. 8%
The velocity of a particle traveling in a straight line is given by v (6t-3t2) m/s, where t is in seconds. Suppose that s 0 when t0. a. Determine the particle's deceleration when t3.6s b. Determine the particle's position when t 3.6 s C. How far has the particle traveled during the 3.6-s time interval? d. What is the average speed of the particle for the time period given in previous part?
The velocity of a particle moving along x-axis is given by v(t) = 4 alpha middot t^2 - beta middot t in m/s. (a) Find the units of measurement of the known constants alpha and beta. (b) Find the average acceleration of the particle during its first 5 s of its motion. (c) When does the particle stop momentarily? (d) How far is the particle from the origin at that instant, if x(t = 0) = 0? (e) Find the...
2. [2] If the velocity at time t for a particle moving along a straight line is proportional to the square root of its position x, write a differential equation that fits this description 3. [4] Show that y(x) = e* - x is an explicit solution to the differential equation dy y2 e2x e* - 2xe* + x2 - 1 on the entire real line = dx
1. (10 pts) A particle moving along a straight line decelerates according to a -kv. This represents a drag-induced deceleration. Determine: a) velocity v as a function of time t b) position s as a function of time t c) velocity v as a function of position s At time t-0, the initial velocity is vo and position is s 0
6. A particle is moving on the line with velocity v(t) = 4t2 - 7t - 2 m/sec where 0 st 5a. Assume that at t = 0, the particles position is 0. a. (2pts) When is the particle at rest? b. (3pts) When is the particle moving in the positive direction for t > 0? C. (4pts) Find the distance traveled between the interval 1 st 33.
the velocity of a particle traveling in a straight line is given by v=(6t-3t^2)m/s, where t is in seconds, if s=0 when t= 0. determine the particles deceleration and position when t=3s. how far has the particle traveled during the 3s time interval and what is its average speed?