Calculate acceleration from the resultant force
Use F = ma on the signed total force rather than one convenient individual force.
Section P1.5.1 · Effects of forces
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Calculate collinear resultants.
- Distinguish acceleration from existing velocity.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the resultant of 10 N right and 4 N left?
What you will learn
- Recall and use resultant force = mass × acceleration.
- State the acceleration direction and convert mass to kilograms.
The F in this equation is the resultant
For a constant-mass body in the ordinary laboratory inertial frame, F = ma uses its resultant force. Rearranging gives a = F/m. With right positive, a 3 kg trolley pulled by 10 N right against 4 N resistance left has F = 6 N and a = 2 m/s² right. Dividing the pull alone by mass would miss the resistance.
Use kg for mass, N for force and m/s² for acceleration. A 500 g mass is 0.500 kg; a 2.0 N resultant gives a = 2.0/0.500 = 4.0 m/s². Units are consistent because one newton is one kg·m/s².
Acceleration follows resultant direction
Force and acceleration are in the same direction for this positive-mass model. A 3 kg body with resultant 6 N left has acceleration 2 m/s² left. It may nevertheless be moving right at that instant and slowing down; its existing velocity does not have to match the acceleration direction.
If the resultant is zero, acceleration is zero and velocity does not change. Non-zero force over a specified interval can be combined with earlier motion methods when the acceleration model is constant. Do not infer a time or final velocity from F = ma alone when the required interval and starting velocity are absent.
Sources for this lesson
Pause and explain
A 3 kg body has 6 N resultant left while moving right. What is its acceleration?
Worked example
A 3 kg trolley is pulled 10 N right against 4 N resistance left. Find acceleration.
Show the worked solution
- Rightward resultant = 10 − 4 = 6 N.
- a = F/m = 6/3 = 2 m/s².
- Acceleration points right with the resultant.
Answer 2 m/s² right.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A 3 kg trolley has 10 N pull right and 4 N resistance left. Find acceleration.
Give me a hint
First find the signed force total on the trolley.
Compare my reasoning
- F = 10 − 4 = 6 N right.
- a = 6/3 = 2 m/s².
- The acceleration is rightward.
2 m/s² right.
Look for these in your work
- Find the resultant.
- State acceleration direction.
A mass of 500 g has a 2.0 N rightward resultant. Find acceleration.
Give me a hint
Use kilograms in F = ma.
Compare my reasoning
- 500 g = 0.500 kg.
- a = 2.0/0.500 = 4.0 m/s².
- It points right with the resultant.
4.0 m/s² right.
Look for these in your work
- Convert mass.
- Use the resultant direction.
A 3 kg body currently moves right but has 6 N resultant left. Calculate acceleration and explain its initial effect.
Give me a hint
Acceleration describes a change in velocity, not necessarily the current direction.
Compare my reasoning
- a = 6/3 = 2 m/s² left.
- That opposes the present rightward velocity.
- The body initially slows while still moving right.
2 m/s² left; it initially slows while moving right.
Look for these in your work
- Calculate the acceleration.
- Separate acceleration from velocity.
Common mistakes
- Use resultant rather than driving force alone.
- Convert grams to kilograms.
- Acceleration direction need not equal current velocity direction.
What can you explain now?
What acceleration does 2 N resultant give a 500 g mass?
Compare with the explanation
4 m/s² in the resultant's direction.
Use mass 0.500 kg before dividing force by mass.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Write a force balance before F = ma and explain a case with opposite acceleration and velocity directions.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.