Free Printable & Interactive Newtons Laws Worksheets - Free Printable

Let’s solve each problem one by one using Newton’s Second Law:
Force = Mass × Acceleration → F = m × a

We can rearrange this formula depending on what we’re solving for:
- To find Force: F = m × a
- To find Acceleration: a = F ÷ m
- To find Mass: m = F ÷ a

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Problem 1:

How much force is needed to accelerate a 1000-kg car at a rate of 3 m/s²?

GIVEN:
Mass (m) = 1000 kg
Acceleration (a) = 3 m/s²

WORK:
F = m × a
F = 1000 × 3
F = 3000 N

ANSWER: 3000 N

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Problem 2:

If a 70-kg swimmer pushes off a pool wall with a force of 250 N, what is her acceleration?

GIVEN:
Mass (m) = 70 kg
Force (F) = 250 N

WORK:
a = F ÷ m
a = 250 ÷ 70
a ≈ 3.57 m/s² (rounded to two decimal places)

ANSWER: 3.57 m/s²

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Problem 3:

Find the mass of a football player who has 1250 N of force and has an acceleration of 1.5 m/s².

GIVEN:
Force (F) = 1250 N
Acceleration (a) = 1.5 m/s²

WORK:
m = F ÷ a
m = 1250 ÷ 1.5
m ≈ 833.33 kg (rounded to two decimal places)

Wait — that seems too heavy for a person! Let’s double-check:

1250 ÷ 1.5 = ?

1.5 × 800 = 1200
1250 - 1200 = 50
50 ÷ 1.5 ≈ 33.33
So total = 800 + 33.33 = 833.33 kg → math is correct, but unrealistic. Maybe it’s a typo in the problem? But since we’re solving as given…

Actually — let’s check units again. 1250 N is reasonable for a push, 1.5 m/s² is slow acceleration — so maybe it’s correct? Or perhaps it’s meant to be 1250 N over time? No — per Newton’s law, if those are the numbers, mass is 833.33 kg.

But wait — maybe I misread. Let me re-read: “has 1250 N of force” — yes. “acceleration of 1.5 m/s²” — yes.

Hmm. Perhaps it’s not a real-life scenario — just a math problem. So we’ll go with the calculation.

ANSWER: 833.33 kg

*(Note: In reality, no human weighs that much — but for the sake of the worksheet, we use the numbers given.)*

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Problem 4:

How much acceleration is given to a 45 kg child with a 0.75N push on a swing?

GIVEN:
Mass (m) = 45 kg
Force (F) = 0.75 N

WORK:
a = F ÷ m
a = 0.75 ÷ 45
a = 0.01666... m/s²
≈ 0.017 m/s² (rounded to three decimal places)

ANSWER: 0.017 m/s²

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Problem 5:

What is the mass of a car that its going 2 m/s² and then hits a tree with a force of 6000N?

This wording is tricky. It says “going 2 m/s²” — that’s acceleration, not speed. And “hits a tree with a force of 6000N”.

In physics, when something hits a tree, the force during impact depends on how quickly it stops — which relates to deceleration. But here, it seems they’re implying that the car was accelerating at 2 m/s² *before* hitting the tree, and the force upon impact is 6000 N.

But actually — if we assume that the 6000 N is the force applied *during* the collision, and the acceleration mentioned (2 m/s²) is the deceleration during impact, then we can use:

F = m × a → m = F ÷ a

So:

GIVEN:
Force (F) = 6000 N
Acceleration (a) = 2 m/s² (assuming this is the magnitude of deceleration during impact)

WORK:
m = F ÷ a
m = 6000 ÷ 2
m = 3000 kg

That makes sense — a car weighing 3000 kg is about 3 metric tons — reasonable for a large vehicle.

ANSWER: 3000 kg

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Final Answer:
1. 3000 N
2. 3.57 m/s²
3. 833.33 kg
4. 0.017 m/s²
5. 3000 kg