Question

A particle starts from the origin at t=0 with an initial velocity of 10m/s along the positive x-axis. If the acceleration is (-6i+4j)m/s determine the velocity and position of the particle as a function of time at the moment it reaches its maximum x-coordinate.

Answer 1

$$v_x=10-6t=0\frac{m}{s}\\t=1.67\ s\\ x=10(1.67)-6(0.5)(1.67)^2=-8.37\ m \\ y=4(0.5)(1.67)^2=5.58\ m \\ v_y=4(1.67)=6.68\frac{m}{s}$$