question in kinematics?

Question

a police car is searching foe a fugitive taht managed to escape a while ago.knowing that he is now safe,the fugitive begins to take a rest until he notices a police car approaching him at 10m/s,accelerating at 5m/s^2 and it is 100m away.the fugitive grabs a motorcycle and starts it accelerating at the same rate as the police car.how mush time will it take the police car to catch the fugitive?

what is the effect of the height of the track(incline) to the cart's acceleration?may answer is this the effect is that the cart move fast because if the height is higher the higher the acceleration too??i'm right if not ,explain to what is the effect of height..

why is that time is related to the inclnation of the track?please expalin to me

thanks again

Answer 1

To answer your first question, if the motorcycle and the car are accelerating at the same rate, the rate at which the distance between them closes depends only on the initial velocity of the police car, so it will take (100 m) / (10 m/s) = 10 s.

In your second question, gravity acts downwards, but the cart accelerates along the surface of the incline, so it is only the component of gravity in that direction that increases the speed of the cart. When the incline is steeper, that component is greater.

Answer 2

OK....

the police car moves with an initial velocity of 10m/sec and accelerates at the same rate as the fugitive that starts at rest .
simply consider that every second that passes the difference in acceleration of these two is zero. it is like the police car moves at in order to cover this extra distance due to the initial velocity factor (Uo*t)

to imagine it otherwise it is like they both start at the same time the same point one has initial velocity and the other starts from rest. so you are called to calculated when the distance between them will be 100m. correct? it is the same problem.


now......

when the police car catches the fugitive

the fugitive distance is = 1/2gt^t
the police car distance is = Uot + 1/2gt^2

but the police care distance is Sfug. + 100m

therefore we rearrange and get that

100 + 1/2 * g*t2 = Uot + 1 / gt^2 and we are interested in t

this becomes.....

t = Uo police car / 100m =>
t = 10 sec.
that makes sense according our original thought (like having somehting moving with constant speed at 10m/s tryng to cover a distance of 100m)


NOW for second part if i understand you want to find the relation of the height of the incline and the acceleration.

first of all since there is a trigonometry present the angle of the incline is very important. the greater the incline the more of weight power resultsas a moving force in the direction of movement.
ideal at 90 degres "all" the weight will be applied and all the acceleration will be g it self. (imagin ia as sin90 = 1 ;) )

now the angle is very important.
the height in a certain angle denotes how long is the incline. simple trigonometry. so for a bid heigh you have a larger path therfore a larger finala velocity at the base
PLEASE NOTE that the acceleration remains the same.
the velocity is larger due to the larger path that the force
Bx was applied.

you can understand it better if you thing it as a potential energy transfromed to kinetic energy as well. so larger heigh larger velocity at the bottm..got it??


the acceleration remains the same though
it is a matter of angle.

cheers