Kinetic energy is the energy an object has because it is moving, and it depends on both how heavy it is and how fast it travels. The formula shows that energy of motion equals one-half times the mass times the velocity squared. The one-half factor and the velocity squared aren’t arbitrary: they come from how much work is required to accelerate an object from rest. Because velocity is squared, speed has a big effect on energy—doubling the speed makes the energy increase by a factor of four, while doubling the mass doubles the energy. Check the units to see it makes sense: kilograms times (meters per second) squared gives kilograms times square meters per second squared, which is joules, the standard unit of energy. The other expressions don’t match kinetic energy: momentum is m v, not energy; potential energy from gravity is m g h; and combining mass with acceleration (1/2 m a^2) mixes variables that describe motion differently and doesn’t represent the energy of motion.

When acceleration is kept constant, force is directly proportional to mass because F = m a. If mass doubles while a stays the same, the product m a doubles, so the force must double. Think of pushing a cart: with the same speed of acceleration, a heavier cart requires a stronger push, exactly doubling the force if the mass doubles. A quadruple force would require something else to change (like acceleration or mass changing by more than a simple doubling); the force staying the same would mean mass or acceleration didn’t change; halving the force would require mass to halve or acceleration to drop. So the force doubles.

A wedge is formed by two inclined planes joined at a thin edge. That edge concentrates force along a sharp line, allowing the wedge to split, cut, or pry apart materials when you drive it in. So describing it as an inclined plane with one or two sloping sides fits a wedge perfectly—the two sloping surfaces meet at the edge to perform tasks like cutting or splitting. The other options don’t fit this description: an inclined plane by itself is just a single ramp, a screw is a spiraled inclined plane around a cylinder, and a compound machine combines multiple simple machines.

t₁ − t₁ represents the amount of time that passes from time t₁ to time t₁. In physics, this duration is called the time interval and is written with the Greek letter Δt. It tells you how long something lasts or how much time elapses between two moments, with units of seconds. If t₁ comes after t₁, Δt is positive; if the moments were swapped, it would be negative, but we usually think of the magnitude as the elapsed time. The other quantities refer to different ideas: Q is heat energy transferred, Cp is the specific heat capacity at constant pressure, and m is mass.