Motion Question

[sxcalexc]

Hey guys after looking at this question my first thoughts were to find the velocity during the 10th second where t=1 but I then realised that it's still accelerating during the second so you can't do v = d/t. I then though about simultaneous equations of motion but I don't think there are enough values. Care to enlighten me?

[Collin Li]

It's accelerating uniformly, so you use the constant acceleration equations of motion. You know that it accelerates from rest () and that in the 10th second of motion, it moves 28.5 m, this means that:

, where is the displacement from the starting point at any time t.

We can find , with this formula:

, but since :



Therefore:

and

Using the above equation: , therefore:

[sxcalexc]

Cheers collin!

Ps. Love the Yoshi

[iamdan08]

Rather than start a new thread I'll post my motion question here:

A car travelling with a constant speed of passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to in 10.0s and reaching a constant speed of after a further 5.0s. At what time will the policman catch up with the car?

Thanks!

[ed_saifa]

40 seconds?

[iamdan08]

The back of the book says 32.5s.

[ed_saifa]

let me check my working.

[ed_saifa]

Did you try a velocity time graph?

[iamdan08]

Yeah i tried to sketch one but i wasn't sure what i was supposed to do from there, or whether you are able to use the equations of motion without drawing a graph.

[ed_saifa]

maybe thats why i keep getting the wrong answer. I kept drawing it on a velocity time graph.

[Collin Li]

Drawing the velocity-time graph should reveal:

1) The first 10 seconds shows the car overtaking the motorcycle. Assuming a constant acceleration, the distance gained (area between two curves) is:



(I have converted the speed into SI units in this single step as well)

2) The next 5 seconds (t=10 to t=15) shows the motorcycle catching up to the car in distance (it's speed is now faster than the car). Assuming constant acceleration again, the distance caught up (area between two curves) is:



So now, the car is only ahead of the motorcycle by 97.2 metres, and the car is catching up at a rate of .

This means that it will take another for the motorcycle to catch up.

This means the total time taken (including the initial 15 seconds we did manually) is .

[iamdan08]

Awsome! Now I understand, thanks heaps!

[Mao]

A more algebraic method:

speed of the car:

Distance by the car (in terms of t):


Acceleration of the police:

Time it took for the police to get to 100km/h:

Distance by the police (in terms of t, partially using x=ut+0.5at²):

equating these two functions in terms of t will arrive at the point when the distance covered are the same, i.e. the police has caught up with the motorcycle.