Variable forces and powerAQA A-Level Further Maths: Flashcards

What these 12 flashcards ask

State the work done by a variable force F(x) from x=a to x=b.
What does the area under a force–displacement graph represent?
Find the work done by F=6x from x=0 to x=3.
How does the work–energy principle apply to a variable force?
Define power.
State the formula linking power, force and speed.
How many watts in 1 kW?
What is the driving force of a 30 kW engine at 20 m s^{-1}?
State Newton's second law for a vehicle with power P and resistance R.
Which formula gives the maximum speed of a vehicle?
Why does acceleration fall as a vehicle speeds up at constant power?
Where is the speed of a particle greatest under a variable force?

Exam questions on Variable forces and power

A particle of mass 2 kg is moved along a straight line from $x=0$ to $x=4$ by a force of magnitude $F=3x^2+2$ newtons acting in the direction of motion, where $x$ is the distance in metres from the starting point. The particle starts from rest and no other force does work.
Find the work done by the force as the particle moves from $x=1$ to $x=3$ .2 marks
A car of mass 1200 kg travels along a straight horizontal road with its engine working at a constant 30 kW. The resistance to motion is a constant 750 N.
Find the acceleration of the car when its speed is $20\text{ m s}^{-1}$ .2 marks
A train of mass 200 000 kg moves along a straight horizontal track. The engine works at a constant 400 kW and the resistance to motion is a constant 8000 N.
Find the acceleration of the train when its speed is $25\text{ m s}^{-1}$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).