M1 Acceleration question...

Hi... I seem to have forgotten one of the first things we did in M1 this year :frown:

A sprinter runs a 200m race. Her total time is 25s. She starts from rest and accelerates uniformly to a speed of 9ms^-1 in 4 seconds. This speed is maintained for 16 seconds and she then decelerates uniformly to a speed u ms^-1 at the end of the race. Calculate:

(a) the distance covered by the sprinter in the first 20s. (2)

Well obviously the 16s at 9ms^-1 makes 144m. I just don't quite get how to work out the initial 4s.

(b) value of u (4)

Constant acceleration formula but impossible without the answer to (a)?

(c)deceleration of the sprinter in tha last 5s (3)

Same again?

Reply 1

phys981

initial 4 seconds

s = ut + 1/2 at2

With u=0, of course

U at the end of the race isn´t zero as she´ll still be moving as she crosses the line.

Once you know how far she ran in the first 20s you can work out how much further she had to run, this is the distance covered as she decelerates.

I´'m still thinking....

Reply 2

phys981

Aha! Missed the total 25s. (RTFQ)

She´s decelerating for 5s, you know by now how much further she has to run, you know her speed just before she starts to decelerate so use

s = ut + 1/2 at2 again to get the acceleration (t =5, u = 9)

then use the acceleration in v2 = u2 + 2as to find the finishing speed, I think.