To calculate acceleration, first find the resultant force. If a driving force acts forwards and resistance acts backwards along the same line, subtract the resistance from the driving force. Then divide by the mass.
The 2027 SEC G3 Physics K323 syllabus covers the relationship between resultant force, mass and acceleration. This worked example shows how a vehicle can keep moving forwards while its acceleration points backwards.
- Choose a positive direction.
- Give each horizontal force a sign.
- Add the forces to find the resultant.
- Use the resultant to calculate acceleration.
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Keep motion and force separate
A cart can be moving forwards while a resistive force acts backwards. The direction of travel tells you the direction of velocity. The resultant force tells you the direction of acceleration. On a level track, the weight and the upward contact force balance vertically if there is no vertical acceleration.
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Worked example | A cart is pulled along a level track
A 40 kg cart has a forward pull of 90 N and a backward resistive force of 30 N. With forwards taken as positive, the horizontal resultant is 90 − 30 = +60 N. The acceleration is +60 ÷ 40 = +1.5 m/s². Dividing 90 N by the mass would leave out the resistance.
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Change the driving force and predict the motion
Suppose the forward pull falls to 20 N while resistance is still 30 N at the instant being considered. The resultant is −10 N and the acceleration is −0.25 m/s². If the cart is still moving forwards at that instant, it slows down. Its velocity does not switch direction immediately.
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Frequently asked questions
What if the two horizontal forces are equal?
The horizontal acceleration is zero. A cart already moving forwards continues at constant velocity while the forces remain balanced.
What can a parent ask during revision?
Ask the student to draw the two horizontal arrows and circle the force value they divide by mass.