at t=0, an object starts to move from rest and moves in the xy plane with the acceleration a=(4.0i+3.0j)m/s^2. determine a) the x and y components of velocity b) the speed of the particle and c) the position of the particle , all as a function of time. d) evaluate all above at t=2.os

a = 4i+3j

v = 4t i + 3t j
speed = |v| = 5t
r = 2t^2 i + 3/2 t^2 j

Did you know?

Did you know that the velocity of an object can be broken down into its x and y components? In this case, the object's acceleration is given as a=(4.0i+3.0j)m/s^2. By integrating the acceleration equation with respect to time, we can find the x and y components of velocity as v_x = 4.0t + C and v_y = 3.0t + D, where t is the time and C and D are constants. To find the speed of the particle, we can use the Pythagorean theorem: speed = √(v_x^2 + v_y^2). By integrating the velocity equations with respect to time, we can find the position of the particle as x = (2.0t^2 + Ct + E)i and y = (1.5t^2 + Dt + F)j, where E and F are constants. If we evaluate all of the above equations at t=2.0s, we can determine the x and y components of velocity, the speed of the particle, and the position of the particle at that specific time.