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Force and Acceleration

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Force and Acceleration

Aotearoa’s school robotics team is testing a small electric cart. Use the evidence and the relationship between force, mass and acceleration to help the team make safe, sensible decisions. Assume friction is negligible unless a question says otherwise. Acceleration is measured in metres per second squared (m/s²).

The key idea

The net force on an object equals its mass multiplied by its acceleration: F = m × a. Force is measured in newtons (N), mass in kilograms (kg), and acceleration in m/s². Rearrange the relationship when needed: a = F ÷ m.

Test-track results

The team tested the cart from rest on the same track. In Tests A and B, the cart’s mass stayed at 2 kg. In Tests A and C, the net force stayed at 6 N.

Test A Net force: 6 N Mass: 2 kg Acceleration: 3 m/s²

Test B Net force: 10 N Mass: 2 kg Acceleration: 5 m/s²

Test C Net force: 6 N Mass: 4 kg Acceleration: 1.5 m/s²

1.Which calculation gives the acceleration in Test A?

2 ÷ 6 = 0.33 m/s²
6 ÷ 2 = 3 m/s²
6 × 2 = 12 m/s²
6 + 2 = 8 m/s²

2.Tests A and B have the same mass. How does increasing the net force from 6 N to 10 N affect the cart’s acceleration?

3.Tests A and C have the same net force. Why does the 4 kg cart in Test C accelerate less than the 2 kg cart in Test A?

4.The team adds equipment so the cart’s total mass is 3 kg. The motor provides a net forward force of 12 N. Calculate the cart’s acceleration. Show your working and include the unit.

5.A loaded cart has a mass of 5 kg and accelerates at 2 m/s². What net force acts on it? Show your working and give the unit.

6.A team member says, “If the cart’s mass doubles and the net force stays the same, its acceleration doubles too.” Is this claim correct? Explain using the force–mass–acceleration relationship.

7.During a run, the motor pushes forwards with 9 N while friction acts backwards with 3 N. The cart’s mass is 2 kg. Calculate the net force and then the acceleration.

8.The cart is moving forwards. Its motor is switched off, and friction is the only horizontal force. What happens to its speed while friction acts? Explain the direction of its acceleration.

9.The team wants to find out how changing mass affects acceleration. Describe a fair test: state what to change, what to measure, and at least one factor to keep the same.

10.The cart and payload have a combined mass of 4 kg. The team can choose a net force of 4 N or 12 N. Which setting gives the smaller acceleration, and what is that acceleration? Give one reason the team might choose it for a first test.