Newton's Second Law (AQA GCSE 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:

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

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

a = 27 ÷ 3 = 9 m/s²

Part (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

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

A passenger travels in a car at a moderate speed. The vehicle is involved in a collision, which brings the car (and the passenger) to a halt in 0.1 seconds.

Estimate:

a) The acceleration of the car (and the passenger).

b) The force on the passenger.

Answer:

Part (a)

Step 1: Estimate the required quantities and list the known quantities

A moderate speed for a car is about 50 mph or 20 m/s

• Initial velocity ~ 20 m/s

• Final velocity = 0 m/s

• Time, t = 0.1 s

Step 2: Calculate the change in velocity of the car (and the passenger)

change in velocity = Δv = final velocity − initial velocity

Δv = 0 − 20

Δv = −20 m/s

Step 3: Calculate the acceleration of the car (and the passenger) using the equation:

Step 4: Calculate the deceleration

a = −20 ÷ 0.1

a ~ −200 m/s²

Part (b)

Step 1: Estimate the required quantities and list the known quantities

An adult person has a mass of about 70 kg

• Mass of the passenger, m ~ 70 kg

• Acceleration, a = −200 m/s²

Step 2: State Newton's second law 

• This question involves quantities of force, mass and acceleration, so the equation for Newton's second law is:

F = ma

Step 3: Calculate an estimate for the decelerating force

F = 70 × −200

F ~ −14 000 N

Remember that resultant force is a vector quantity.

Examiners may ask you to comment on why its value is negative - this happens when the resultant force acts in the opposite direction to the object's motion.

In the worked example above, the resultant force opposes the passenger's motion, slowing them down (decelerating them) to a halt, this is why it has a minus symbol.