Newton's Second Law (Cambridge O Level Physics)

A car salesman says that his 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:

 (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

change in velocity = Δv = final velocity − initial velocity

Δv = 27 − 0 = 27 m/s

Step 3: State the equation for acceleration

Step 4: Calculate the acceleration

(b)

Step 1: List the known quantities

• Mass of the car, m = 900 kg
• Acceleration, a = 9 m/s²

Step 2: Identify which law of motion to apply

• The question involves quantities of force, mass and acceleration, so Newton's second law is required:

F = ma

Step 3: Calculate the force required to accelerate the car

F = 900 × 9 = 8100 N

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

Which trolley will 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