Physics

Force and Motion

6,184 words, 10 sections

This chapter is the mechanics core of the physics paper: how position, velocity and acceleration are defined and related, how Newton's three laws explain why objects speed up, slow down or change direction, and how momentum accounting solves collisions and explosions that Newton's third law alone will not. The MDCAT examines it very heavily, with 472 distinct questions across 92 official papers between 2001 and 2026, set by every board that sits the paper. A mean item difficulty of 1.88 on the bank scale marks it as slightly harder than average, and the 1,518 active questions in the practice bank show how central it remains. A student who has mastered this material can read any motion graph, apply the equations of motion without hesitating over signs, and run a momentum balance through a collision or an explosion, which together secure a large block of the paper.

Mechanics starts by separating two quantities that everyday language blurs. Distance is a scalar: how much ground was covered, with no direction. Displacement is a vector: the straight-line change in position from start to finish, with a direction. A runner who goes 600 m north and then 300 m south has travelled a distance of 900 m but has a displacement of only 300 m north. From these come two averages. Average speed is distance divided by time; average velocity is displacement divided by time. The two are equal only when the motion is along a straight path without reversal, because only then does the path length equal the displacement. The speedometer reading at an instant is the instantaneous speed, and the instantaneous velocity on a curved path points along the tangent to the curve at that point.

Acceleration is the rate of change of velocity, $a = (v_f - v_i)/t$ , and it is a vector, so a body can accelerate by changing direction even at constant speed. Uniform acceleration means the velocity changes by equal amounts in equal intervals of time, so the force producing it must be constant; variable acceleration means the velocity changes by unequal amounts, so the acceleration itself is changing. Free fall near the Earth is the standard case of uniform acceleration.

The graphs carry this information compactly, and the examiner reads them constantly. On a displacement-time graph the slope is the velocity: a straight line means constant velocity, and a slope that keeps increasing means the velocity is growing steadily, that is uniform acceleration. On a velocity-time graph the slope is the acceleration, so a horizontal line means constant velocity and a straight sloping line means constant acceleration. The area between the velocity-time line and the time axis is the displacement.

Worked example

A particle is at the 40 m mark at $t = 10\ \text{s}$ and at the 20 m mark at $t = 15\ \text{s}$ . Find its average velocity over the interval. Average velocity is displacement over time, so $v_{\text{avg}} = \dfrac{x_f - x_i}{t_f - t_i} = \dfrac{20\ \text{m} - 40\ \text{m}}{15\ \text{s} - 10\ \text{s}} = \dfrac{-20\ \text{m}}{5\ \text{s}} = -4\ \text{m s}^{-1}$ . Sanity check: the particle moves from a larger coordinate to a smaller one, so the velocity must be negative, and a magnitude of 4 m s $^{-1}$ is a walking pace, which fits the timings. The step students get wrong is taking the sizes only and answering $+4\ \text{m s}^{-1}$ ; the sign carries the direction, and here the direction is backwards along the axis.

8 more sections in this chapter

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Introduction

1. Describing motion: displacement, velocity, acceleration and their graphsMechanics starts by separating two quantities that everyday language blurs. Distance is a scalar: how much ground was covered, with no direction. Displacement i