AMC 10 2021a Problem 4

A cart rolls down a hill, travelling $5$ inches the first second and accelerating so that during each successive $1$-second time interval, it travels $7$ inches more than during the previous $1$-second interval. The cart takes $30$ seconds to reach the bottom of the hill. How far, in inches, does it travel? $\textbf{(A)} ~215 \textbf{(B)} ~360 \textbf{(C)} ~2992 \textbf{(D)} ~3195 \textbf{(E)} ~3242$