Physics

Physics

Problem

A 2 kg2\,\text{kg} ball is moving horizontally at 10 m s−110\,\text{m\,s}^{-1} to the right. A constant horizontal force of 30 N30\,\text{N} acts on it to the left for 0.5 s0.5\,\text{s}. Neglecting all other forces, what is the speed of the ball immediately after the force ceases? a) 17.5 m s−117.5\,\text{m\,s}^{-1} b) 2.5 m s−12.5\,\text{m\,s}^{-1} c) 7.5 m s−17.5\,\text{m\,s}^{-1} d) 5.0 m s−15.0\,\text{m\,s}^{-1}
Intuitive explanation

The key is recognizing that a force changes momentum over time, not just speed directly. Use the impulse-momentum theorem: the impulse (F⋅ΔtF \cdot \Delta t) equals the change in momentum (m⋅Δvm \cdot \Delta v). Since the force opposes the ball's motion, it will slow the ball down—and you need to check whether it reverses direction entirely. Set up a consistent sign convention, calculate the velocity change, and find the final speed.

Intuitive explanation

The key is recognizing that a force changes momentum over time, not just speed directly. Use the impulse-momentum theorem: the impulse (F⋅ΔtF \cdot \Delta t) equals the change in momentum (m⋅Δvm \cdot \Delta v). Since the force opposes the ball's motion, it will slow the ball down—and you need to check whether it reverses direction entirely. Set up a consistent sign convention, calculate the velocity change, and find the final speed.

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