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Mechanics 1 questions..hardish..

Hello I have a few mechanics questions..

(1) A freight train 1/4 mile long takes 20 seconds to pass a signal. The train is decelerating at a constant rate, and by the time the rear truck has passed the signal it is moving 10 miles per hour slower than it was when the engine reached it. Find the deceleration in mile-hour units and the speed at which the train is moving when the rear truck has just passed the signal.

(2) A cheetah is pursuing an impala. The impala is running in a straight line at a constant speed of 16m/s. The cheetah is 10m behind the impala, running 20m/s but tiring, so that it is decelerating 1m/s. Find an expression for the gap between the cheetah and the impala t seconds later. Will the impala get away?


Thanks a lot
From John
for 1 I think the anwer is -40mph. to work this out i used common sense if the train is 1/4 mile lond, and it is going 10mph slower after -10/0.24 = 40.
Reply 2
Write out what you know and find the right equation to use.

eg.
s=0.25milesu=xv=x10a=?t=0.0055hr\huge s=0.25 miles \\ u=x \\ v=x-10 \\ a=? \\ t=0.0055hr

First use s=((v+u)t)/2 to find x, then any other to find a.

Same idea with (2).
Reply 3
Lusus Naturae
Write out what you know and find the right equation to use.

eg.
s=0.25milesu=xv=x10a=?t=0.0055hr\huge s=0.25 miles \\ u=x \\ v=x-10 \\ a=? \\ t=0.0055hr

First use s=((v+u)t)/2 to find x, then any other to find a.

Same idea with (2).


Thanks a lot I managed to do (1) but (2) i cant seem to start off, do you mind helping..

Thanks
From John
For the cheetah, note down what you have, and let t=t as you need to include it in your equation. When they start 10m apart, assume t=0. Write an equation for the cheetah's distance travelled.

Now for the impala. It travels at constant speed. Write down an equation for its distance but remember to add 10, as when t=0, its position is 10m.

The distance between them is (impala - cheetah).
Reply 5
Use for Impala:
s=v+u2t\huge s= \frac{v+u}{2}t Then add +10.
And for Cheetah:
s=ut+12at2\huge s= ut + \frac{1}{2}at^2

As Silent Ninja said, distance between them is (impala - cheetah).
Hopefully you know how to see whether a quadratic has any solutions or not :smile: