Newton's Second Law (Oxford AQA IGCSE Physics): Revision Note

A car salesperson says that their best car has a mass of 900 kg and can accelerate from 0 to 27 m/s in 3 seconds.

Calculate:

(a) The acceleration of the car in the first 3 seconds.

(b) The force required to produce this acceleration.

Answer:

Part (a)

Step 1: List the known quantities

• Initial velocity = 0 m/s

• Final velocity = 27 m/s

• Time, t = 3 s

Step 2: Calculate the change in velocity

$∆v=v_f-v_i$

$∆v=27-0$

$∆v=27\mathrm{m}/\mathrm{s}$

Step 3: State the equation for acceleration

$a=\frac{∆v}{t}$

Step 4: Calculate the acceleration

$a=\frac{27}{3}$

$a=9\mathrm{m}/{\mathrm{s}}^2$

Part (b)

Step 1: List the known quantities

• Mass of the car, m = 900 kg

• Acceleration, a = 9 m/s²

Step 2: State the equation for Newton's second law

$F=m\times a$

Step 3: Calculate the force required to accelerate the car

$F=900\times 9$

$F=8100\mathrm{N}$

Three shopping trolleys, A, B and C, are being pushed using the same force. This force causes each trolley to accelerate.

State which trolley would have the smallest acceleration. Explain your answer.

Answer:

Step 1: Identify which law of motion to apply

• The question involves quantities of force and acceleration, and the image shows trolleys of different masses, so Newton's second law is required:

$F=ma$

Step 2: Re-arrange the equation to make acceleration the subject

$a=\frac{F}{m}$

Step 3: Explain the inverse proportionality between acceleration and mass  

• Acceleration is inversely proportional to mass

• This means for the same amount of force, a large mass will experience a small acceleration

• Therefore, trolley C will have the smallest acceleration because it has the largest mass