How to solve velocity and sector problem?

Question

An airplane egine is idling at 800 rpm. When the throttle is opened, it takes 4.3 secs. for the speed to come up to 2500rpm. What was the angular acceleration (a) in rpm per sec.? (b) in radians per sec per sec.?

Answer 395.35rpm/sec;2484.05rad-min/sec;414rad/sec2
I cant figure out how to work problem out.

Answer 1

I don't get the same answer for the second one.

Same formula as for regular velocity and acceleration. Different letters, though.

ω = ω0 + αt
2500 rpm = 800 rpm + α(4.3 sec)
1700 rpm = (4.3 sec)α
395.35 rpm/s = α

But this is a rather odd unit... rpm is revs/min so you've got revs per minute per second...but that's what they ask for so I'll go with that.

However....for the second question, they ask for radians per second per second, NOT radians per minute per second.

To convert to radians per second per second, I think the answer SHOULD be:

395.35 revolutions/minute/s × 2π radians/revolution × 1 minute/60 seconds = 13.178π radians per second² = 41.4 rad/s²

The answer that they give is in radians per minute-second, which is odd, but if that's what they want, then it's 41.4 × 60 = 2,484.05 rad/min-s, as Benoit got and as your answer shows.

Answer 2

acceleration = (v2-v1)/t
= (2500rpm - 800rpm) / 4.3s
= 395.35 rpm/s

Now 1 rpm = 2pi rad/s, so multiply the above by 2pi to get
2,484.05 rad/s²

I stand corrected Jim, that should be 1 rpm = 2pi rad/min, so my answer should be 2,484.05 rad/min-sec. There seems to be an error in the question (rad/s² when the answer is given in rad/min-sec).