why is the rate of fall 32 feet per second squared instead of 16 feet per second squared since 16 feet is how far it fell in the first second ?

Question

a falling object falls 16 ft. in the first second, so why is the rate of fall not 16 ft. per second squared instead of 32 feet per second squared ?

Answer 1

Objects fall under gravity at an accelerating rate of 32 feet per second per second. That means the speed is changing at the rate of (32 ft/sec) per second. An object which is simply dropped (not thrown) will pick up speed so that after the first second it will be travelling at 32 feet per second. After the second second its speed will have reached 64 feet per second. That's how the speed changes, but what about the distance? To calculate this we start with a speed of zero since we only just let the object fall. After one second the speed is 32 feet per second, so its average speed over the first second is half of the sum of the speed at the start and the speed after one second=1/2(0+32)=16 ft/sec. That's why in one second the object only travels 16 feet. How far does it travel in 2 seconds? This time the average speed is 1/2(0+64)=32 f/s so the distance travelled in 2 secs is 64 feet. How far did it travel between the first and second seconds? Average speed is 1/2(32+64)=48 feet per second. So between the 1st and 2nd second it travelled 48 feet. 48+16=64. The acceleration is constant but the speed varies proportionately. This gives rise to the equation s=1/2at^2 for every object falling under its own weight without being thrown, where a is the acceleration due to gravity and t=time. Put t=2 and a=32 in this equation and you can see it fits the calculations.