Engineering Kinematic
posted by Claire .
The particle travels along the path defined by the parabola y=0.5(x^2). If the component of velocity along the xaxis is v=5t [m/s], determine the particle's distance from the origin and the magnitude of its acceleration when t=1s. The initial condition is t=0, x=0 and y=0.
Can someone please tell me tha answers and how to work it please?

When t = 1, dx/dt = 5t = 5 m/s
From v = dx/dt = 5t, and the starting conditions, you can conclude that
x = (5/2)t^2.
x = 5/2 = 2.5 when t = 1
y = 0.5*(2.5)^2 = 3.125 when t = 1
The distance from the origin in sqrt[x^2 + y^2]. At t=1, this is
D = sqrt[2.5^2 + 3.125^2]= 4.002
The acceleration components are
a_x = d^2x/dt^2 = dv_x/dt = 5 @t=1)
and
a_y = d^2y/dt^2 = dv_y/dt
v_y = dy/dt = dy/dx*dx/dt = x*v_x =
a_y= dv_y/dt = (v_x)^2 + a_x*x
= 25 + 5*1 = 30
Respond to this Question
Similar Questions

physics
In the figure, particle A moves along the line y = 29 m with a constant velocity of magnitude 3.5 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and … 
Physics
In the figure, particle A moves along the line y = 26 m with a constant velocity of magnitude 2.6 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and … 
physics help
The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time … 
physics help
The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time … 
Calculus based physics
A particle travels along a path described by the function y=0.2x^3. The exponent of velocity is given by vx=(5t^2)ft/s. When t=0, x=y=0, find the particle's distance from the origin and the magnitude of its acceleration when t=1s. 
DYNAMICS
A particle travels along a straight line with a velocity v=(123t^2) m/s, when t is in seconds. When t=1s, the particle is located 10m to the left of the origin. Determine the accelaration when t=4s, the displacement from t=0 to t=10s, … 
Physics
One component of a magnetic field has a magnitude of 0.0445 T and points along the +x axis, while the other component has a magnitude of 0.0725 T and points along the y axis. A particle carrying a charge of +1.01 × 105 C is moving … 
Physics
One component of a magnetic field has a magnitude of 0.0445 T and points along the +x axis, while the other component has a magnitude of 0.0725 T and points along the y axis. A particle carrying a charge of +1.01 × 105 C is moving … 
Physics
A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the vaxis scale is set by vs = 7.0 m/s. (a) What is the coordinate … 
univercity of baghdad
A particle travels along a straight line with a velocity v=(123t^2)m/s.where t is in the seconds. When t=1s.the particle is located 10m to the left of the origin. Determine the acceleration when t=4s.the displacement from t=0s to …