Motion, Force and Newton's Laws: Formulas and Facts

The correct answer is A, the law of inertia. The first law states that a body continues in its state of rest or of uniform motion in a straight line unless an unbalanced external force acts on it, which is exactly the property called inertia.

Option B refers to the second law, which deals with the rate of change of momentum and yields the equation force equals mass times acceleration. Option C is the third law, which says that action and reaction are equal and opposite and act on different bodies. Option D, the law of gravitation, is a separate law of Newton's, stating that every body attracts every other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. The first law also defines force, by telling us that a force is what is needed to change a state of motion.

The correct answer is C, displacement. It is the shortest distance from the starting point to the finishing point together with the direction of that straight line, so it has both magnitude and direction and is therefore a vector.

Option A, distance, is the total length of the path travelled and carries no direction, so it is a scalar; option B, speed, is distance divided by time and is a scalar for the same reason, while velocity, which is displacement divided by time, is a vector. Option D, time, is a scalar. The standard illustration is a runner completing one lap of a circular track: the distance covered equals the circumference, but the displacement is zero because the runner ends where the lap began. Remember the pairs, distance with speed as scalars and displacement with velocity as vectors.

The correct answer is B, the second law. It states that the rate of change of momentum of a body is proportional to the applied force and takes place in the direction of the force. Since momentum is mass times velocity, the rate of its change for a body of constant mass is mass times acceleration, which gives the equation force equals mass times acceleration.

Option A, the first law, tells us only that a body keeps its state unless an unbalanced force acts, and so defines force without measuring it. Option C, the third law, deals with the pairing of action and reaction on two different bodies. Option D belongs to a different branch of the subject altogether. The second law also gives the definition of the newton, which is the force that gives a mass of one kilogram an acceleration of one metre per second squared.

The correct answer is B, linear momentum. Before firing, the gun and the bullet are at rest, so the total momentum of the system is zero. No external force acts along the barrel, so the total must stay zero: the bullet leaves with a large forward momentum and the gun acquires an equal momentum backwards, which is felt as the recoil. Because the gun is far heavier than the bullet, its backward velocity is small.

Option A, energy, is conserved in the wider sense but does not by itself give the direction and size of the recoil. Option C, mass, and option D, charge, are also conserved quantities but are irrelevant here. The same principle explains rocket propulsion, where hot gases are pushed out at high speed and the rocket moves the other way, and it is equally the third law of motion seen from another side.

The correct answer is C, the kilogram metre per second. Momentum is the product of mass and velocity, so its unit is the unit of mass multiplied by the unit of velocity, that is kilogram multiplied by metre per second. It is a vector, pointing in the direction of the velocity.

Option A, the newton, is the unit of force, which is the rate of change of momentum rather than momentum itself; a newton is in fact one kilogram metre per second squared. Option B, the joule, is the unit of work and energy. Option D, the newton per second, is not a standard unit at all, although newton second is an acceptable alternative form for momentum because force multiplied by time equals change of momentum, the quantity called impulse. That link between impulse and momentum is itself a favourite examination point.

The correct answer is B, inertia of motion. While the bus is moving, the passenger's whole body moves with it. When the brakes are applied, the feet stop along with the floor of the bus, but the upper body tends to keep moving forward at the same speed, and the passenger is thrown forward.

Option A, inertia of rest, explains the opposite case: a passenger falls backward when a stationary bus starts suddenly, because the body tends to remain at rest. Option C, inertia of direction, explains why mud flies off tangentially from a spinning wheel or why a passenger leans outward when the bus turns. Option D, centripetal force, is the force directed towards the centre that keeps a body on a circular path and has nothing to do with braking in a straight line. All three kinds of inertia are asked through everyday examples like these.

The correct answer is A. The three equations of uniformly accelerated motion are v equals u plus at, s equals ut plus half of a t squared, and v squared equals u squared plus twice a s, where u is the initial velocity, v the final velocity, a the acceleration, t the time and s the distance covered.

Option B replaces time with distance in the first equation, which is wrong because the first equation connects velocity with time, not with distance. Option C omits the half and squares nothing, so it is not the second equation. Option D squares the time in the first equation, which belongs to the second equation instead. The third equation is the useful one when time is not given, and the choice of equation in a numerical question is decided entirely by which of the five quantities the problem does not mention.

The correct answer is B, displacement. On a velocity-time graph the height of the curve is velocity and the base is time, so the area enclosed is velocity multiplied by time, which is displacement.

Option A, acceleration, is given by the slope of the same graph, not by its area, and mixing up slope and area is the commonest error in this question. Option C, force, and option D, momentum, cannot be read off a velocity-time graph at all unless the mass of the body is also given. The companion result is worth learning in the same breath: on a distance-time graph the slope gives the speed, so a straight sloping line means uniform speed and a horizontal line means the body is at rest. Papers often show a simple graph and ask for one of these three readings.

The correct answer is B. The third law says that to every action there is an equal and opposite reaction, and the crucial point is that the two forces act on two different bodies. A swimmer pushes the water backward and the water pushes the swimmer forward; the first force acts on the water and the second on the swimmer.

Option A states the popular misunderstanding: forces can cancel only when they act on the same body, so if action and reaction acted on the same body nothing would ever move. Option C contradicts the law, which insists the two are equal in magnitude. Option D reverses the direction; they are exactly opposite. Other standard examples are the recoil of a gun, the movement of a rocket as gases are pushed out behind it, and the backward push of the ground felt when walking.

The correct answer is A, speed. The slope of any graph is the change on the vertical axis divided by the change on the horizontal axis; here that is distance divided by time, which is speed by definition.

Option B, acceleration, is the slope of a velocity-time graph, not of a distance-time graph, and this is the pair that examiners deliberately confuse. Option C, distance, is read from the vertical axis directly and is not a slope at all. Option D, momentum, cannot be obtained from such a graph without the mass. Two shapes are worth recognising at sight: a straight sloping line on a distance-time graph means uniform speed, and a line parallel to the time axis means the body is stationary, while a curve of increasing slope means the body is speeding up.

The correct answer is B, its mass. Inertia is the tendency of a body to resist any change in its state of rest or of uniform motion, and the heavier the body the harder it is to start or to stop. For this reason mass is described as the measure of inertia.

Option A, velocity, does not alter inertia: a stationary truck and a moving truck of the same mass are equally hard to accelerate. Option C, shape, changes air resistance and the distribution of matter but not the inertia associated with straight line motion. Option D, the applied force, decides the acceleration produced, not the inertia the body already possesses. A useful everyday comparison is that a loaded truck is much harder to push into motion, and much harder to bring to a halt, than a bicycle of the same make of wheel.

The correct answer is B. Whether the hands are moved or not, the momentum of the ball must be brought down to zero. By the second law of motion the force is the change of momentum divided by the time taken, so stretching the catch over a longer time means a smaller force on the hands, and the catch does not hurt.

Option A is wrong because the fielder is removing momentum, not adding it. Option C is impossible; the mass of the ball cannot change. Option D confuses the issue, since the fielder reduces the rate at which the velocity changes rather than increasing it. The same idea explains a number of familiar safety measures: helmets and padded dashboards lengthen the time of impact, an athlete lands in a sand pit rather than on hard ground, and a person jumping down bends the knees on landing.