A car is traveling along a road, and its engine is turning over with an angular velocity of +200 rad/s. The driver steps on the accelerator, and in a time of 13.0 s the angular velocity increases to +300 rad/s. (a) What would have been the angular displacement of the engine if its angular velocity had remained constant at the initial value of +200 rad/s during the entire 13.0-s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +300 rad/s during the entire 13.0-s interval? (c) Determine the actual value of the angular displacement during the 13.0-s interval.

a) +2600 rad

b) +3900 rad

c) +3250 rad

Explanation:

a)

The angular velocity of an object in rotation is given by

where

is the angular dispalcement

t is the time elapsed

In this problem:

is the constant angular velocity of the engine during the time interval

t = 13.0 s is the time elapsed

Therefore, re-arranging the equation, we can find the angular displacement:

b)

In this case, instead, we have:

is the constant angular velocity during the time interval

t = 13.0 s is the time elapsed

We can use again the same equation as before:

where

is the angular dispalcement

t is the time elapsed

And solving for the angular displacement, we find:

c)

In this case, the motion of the engine is accelerated, so we can use the equivalent of the suvat equations for rotational motion; we can use:

where:

is the initial angular velocity

is the final angular velocity

t is the time elapsed

For the engine in this problem we have:

t = 13.0 s

Therefore, the angular displacement of the engine is:

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

well, you would divide 135 by 33 to get your answer. then that is how many seconds it would take. boardman should fly about 132 m or 4.090909090909091 seconds.