CAIE A-Level Mathematics A2 4.5.4 Power in Mechanical Systems

[Maximum number: 5]

A cyclist is travelling along a straight horizontal road. The total mass of the cyclist and her bicycle is 80 kg . There is a constant resistance force of magnitude 32 N to the cyclist's motion. At an instant when she is travelling at $7 \mathrm{~ms}^{-1}$ , her acceleration is $0.1 \mathrm{~ms}^{-2}$ .

(a)

Find the power output of the cyclist.

[ 3 ]

$D F=\frac{P}{7}$
For $P=D F \times 7$ OE seen at any point in working.

Marking guidance:

Allow any force term or simply D F,
e.g. $32,80 \times 0.1,32-80 \times 0.1,80 \times 10$ etc.

$D-32=80 \times 0.1$
For use of Newton's second law. Must have correct number of
terms. Allow sign errors.

[Power = ] 280 W

(b)

Find the steady speed that the cyclist can maintain if her power output and the resistance force are both unchanged.

[ 2 ]

[At steady speed driving force =] $32=\frac{280}{v}$

M1

Attempt at equilibrium equation ( a=0 ) with their power.

Steady speed $=8.75 \mathrm{~ms}^{-1}$ or $\frac{35}{4} \mathrm{~ms}^{-1}$

A1FT

OE

FT their power from part (a) $\frac{\text { their } 280}{32}$ .

CAIE A-Level Mathematics A2 4.5.4 Complex Loci Questions

Exam points

CAIE A-Level Mathematics A2 4.5.4 Complex Loci Questions question 1

Question (a)

Question (b)