Acceleration without a time?

Question

Firing men in a capsule from a 220 meter long cannon with final speed of 10.97 km/s. What is the acceleration?

I'm confused on how to find the acceleration without a time given, and I tried to calculate the time, and was not successful...

Any help would be appreciated!

Answer 1

I'm going to assume the man in the capsule isn't moving until the cannon is fired, and the acceleration is constant. Since the acceleration is constant, the AVERAGE speed is 1/2 of the 10.97 = 5.485.

Speed = distance/time. 5.485 = 220 m/t; time = 40.1 s.

Then plug it into d = 1/2 * a * t^2

Done!

Answer 2

The way to find the time is first to note that the average speed through the cannon is just the average of the beginning and ending speeds (this assumes acceleration is constant).  That is:

average speed = (v_initial + v_final) / 2

= (0 + v_final) / 2

= v_final / 2

Second, use this formula:

time = (distance) / (average speed)

= (distance) / ½ v_final

= 2×distance / v_final

Answer 3

2 a d = v²

a = v² / 2 d = ( 10 970 m/s )² / ( 2 ) ( 220 m ) = 270,000 m/s²

The men do not survive this process.