Question
A block of mass rests on a frictionless horizontal surface. A horizontal force is applied to it. Find the acceleration of the block and the distance covered in 4 seconds, starting from rest.
Solution — Step by Step
Newton’s second law gives us . The surface is frictionless, so the only horizontal force is the applied . No need to resolve anything — the geometry is one-dimensional.
The direction of matches the direction of — that is the whole content of the second law in 1D.
Initial velocity , . From :
Acceleration , distance .
Why This Works
Newton’s second law is a recipe: net force divided by mass gives acceleration. Once we know is constant (the force is constant, mass does not change), the SUVAT equations from kinematics take over.
We do not need to track the normal force or weight in a horizontal-surface problem — they cancel vertically and contribute nothing horizontally on a frictionless floor.
Alternative Method
Using work-energy theorem: work done . Final KE , where . So , giving . Same answer, longer route. We use this when force is variable, not for clean Newton’s-law setups.
Common Mistake
Students often write and try to “balance” forces vertically when the question is purely horizontal. The vertical balance () does not enter the calculation here at all — only horizontal produces horizontal . Keep axes separate from day one.