A particle starting from rest accelerates according to the equation a = 5t2, where a in ft per second square and t in seconds. Five seconds later, its acceleration increases linearly up to 100ft per second square for 3 seconds. In 8 seconds, it travels at constant acceleration for 5 seconds and afterwards decelerates linearly up to zero feet per second square for 7 seconds. Sketch the a-t, v-t, and x-t curves and solve for the average velocity of the particle.

A particle starting from rest accelerates according to the equation a = 5t2, where a in ft per second square and t in seconds. Five seconds later, its acceleration increases linearly up to 100ft per second square for 3 seconds. In 8 seconds, it travels at constant acceleration for 5 seconds and afterwards decelerates linearly up to zero feet per second square for 7 seconds. Sketch the a-t, v-t, and x-t curves and solve for the average velocity of the particle.