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## Homework Statement

bicyclist increases its velocity at constant power

a) how great is this power when the bicycle's velocity increases, from 18km/h to 23km/h, during the time of 1,2 seconds

b) Within which boundaries does the acceleration vary? The combined mass of bicyclist and his bicycle is 78kg

## Homework Equations

delta E= W

0,5 * m * v^2 = E

_{kin}

## The Attempt at a Solution

a)

I assumed the same mass of bycyle as it was described in the later b) portion of the problem. Assume mass = 78kg

The problem looks like very difficult to solve, without assuming the mass to be 78kg. I wonder whether it is possible to calculate the power, without this beginning assumption.

transform velocities into m/s

v0= 5 m/s (nice that it divided evenly by 3,6!)

v1= 6,388 m/s

delta E

_{kinetic}= Work

work = 616,4552 joules

assuming flat ground during travelling.

P=W/t

P= 616,4552 joules / 1,2 s

P= 513,71 Watts

roughly 510 Watts (correct answer according to book answer, in this sense)b) Within which boundaries does bicycles acceleration vary?

I have no idea how to strictly speaking answer the b) part

I suppose one could examine the velocities v0 and v1.

It is known that v0= 5m/s and v1= 6,388m/s

I backtracked in my textbook and found a formula which seems useful in this case. I must have glazed over this formula or simply misunderstood the formula earlier.

Ok according to my physics book one can calculate thusly

power at instant = (force at instant) * (velocity at instant)

We already calculated the power which was 510 Watts.

If we assume constant power, then we could use

P = F * v

510 W = F1* 5 m/s

510 W = F2 * 6,388 m/s

F1= 102 N

F2= 79, 8371 N

F= ma

Then we can know already the mass, and the forces F1 and F2.

We can calculate a1 and a2

F1= m*a1

F2= m * a2

a1= 102N / 78kg

= 1,3076 m/s^2

a2= 79,8371 N / 78kg

=1,0235 m/s^2