A particle moves with constant acceleration and its velocity at time t :
v= (5-0.1t)i +(3+0.2t)j
1. find a, u
2. find the time t when particle is travelling in direction NE and find its speed.
3. find the distance and bearing of the particle from the starting point at that time.
- nyphdinmdLv 71 month ago
acceleration = dv/dt = a = -0.1 *i +0.2 j
u = position = Integral(v dt) = (5t - 0.05t^2)*i + (3t + 0.1t^2)*j +u0 where u0 is a constant vector
Define NE as 45deg north of east and let the i direction be pointing east, and the j diretion pointing north. THen
45 = arctan(u_y/u_x) or tan(u_y/u_x) = 1 --> uy/u_x = pi/4 (radians)
uy = pi*u_x/4 ---> 3t + 0.1t^2 = pi*(5t - 0.05t^2)/4
re-arrange --> 3t + 0.1t^2 - pi*(5t - 0.05t^2)/4 = 0
divide out a t --> 3 + 0.1t - pi*(5 - 0.05t)/4 = 0
3-5*pi/4 +(0.1 +0.05*pi/4) t = 0 --> t = (5*pi/4 - 3)/(0.1 +0.05*pi/4)
plug into your calculator for t.
Speed is |v| = sqrt((5-0.1t)^2 +(3+0.2t)^2) using value of t found above
For starting point - let starting point be at (0,0) --> u0 = 0 i + 0 j
Distance is then |u(t) - u0| = sqrt((5t - 0.05t^2)^2 +(3t + 0.1t^2)^2) evaluated at the value of t you found above
- 1 month ago
a=-0.1i+0.2j, u= v at t=0 =5i+3j, NE is 45 degree. it is obvious. I strugle to find t in question 2. Thanks