2. The velocity of a particle moving along a horizontal line is given by v(t) =...
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
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)....
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.
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
The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) t 4 5, 0sts 10 v(0) (a) Find the velocity at time t. 2 4t5 2 v(t) m/s (b) Find the distance traveled during the given time interval. 416.6 Need Help? Talk to a Tutor Read It Watch It
The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) t 4 5,...
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...
A particle moves along a straight line and its position at time t is given by s(t)= 2t^3 - 21 t^2 + 60 t where s is measured in feet and t in seconds.a) Find the velocity (in ft/sec) of the particle at time t=0:The particle stops moving (i.e. is in a rest) twice, once when t=A and again when t=B where A < B.b) A isc) B isd)What is the position of the particle at time 14?e)Finally, what is...
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.]
A particle P moves along a straight line in such a way that at time t seconds its velocity v m s^-1 is given by v = 1/2 t^2 - 3t + 4 Find the times when P is at rest. the total distance travelled by P between t = 0 and t = 4.
The position of a particle moving along the x axis is given by x= 6.0.-1.0p, where x is in meters and ria seconds. What is the position of the particle when it achieves its maximum speed in the positive x direction? a. 32m b. 12m c. 16 m d. 24 m c. 2.0m 12. 13. The position of a particle moving along the x axis is given by x (21 +221-6.0)m, where t is in s. What is the average...