When time is the independent variable and position is the dependent variable, the slope m tells how quickly position changes as time passes. That rate of change is velocity. In a linear relation y = m x + b, if x represents time, then the slope m is the velocity, since it equals dy/dt. The larger the slope, the faster position changes per second; the units work out to meters per second (assuming y is in meters and x in seconds). The intercept b simply represents where the object is at time zero, not how fast it’s moving. Acceleration, on the other hand, is the rate at which velocity itself changes with time, which would require the slope to change with x; here the slope is constant, so acceleration is zero in this straight-line motion.

In collisions with no external forces, momentum is conserved. If the two 0.5 kg balls stick together, the total mass after the collision is 1.0 kg. The initial momentum comes only from the moving ball: p_i = (0.5 kg) × u = 0.5u. After sticking, they move as a single 1.0 kg object, so (1.0 kg) × v = 0.5u, giving v = 0.5u. So the final velocity is half of the initial velocity. (Kinetic energy isn’t conserved in inelastic collisions—the momentum is, but some energy is lost to deformation, heat, etc.)

In a collision, the total energy of the system, if you account for all forms of energy, stays the same. That means kinetic energy, internal energy, deformation energy, heat, sound, and other forms can exchange energy among themselves, but the sum remains constant. If the bodies deform or heat up, some of the kinetic energy is converted into other forms, so the kinetic energy after the collision is not the same as before. Only in an ideal elastic collision would the kinetic energy be preserved as well. So the best statement is that total energy is conserved in all collisions, but kinetic energy may not be. The idea to keep in mind is that energy can change form during a collision, but the total amount doesn’t vanish or appear from nowhere. The other options either claim kinetic energy is always conserved (which isn’t true for inelastic collisions) or claim momentum is conserved in every collision without qualification (external forces can affect momentum exchange), or say energy can be created or destroyed (which would violate energy conservation).

The key relation here is the mirror equation that links focal length, object distance, and image distance for a concave mirror. Using 1/f = 1/do + 1/di with f = 0.20 m and do = 0.30 m, you solve for di: 1/di = 1/f − 1/do = 1/0.20 − 1/0.30 = 5 − 3.333… = 1.666…, so di = 0.60 m. The positive di means the image is real and forms in front of the mirror. The magnification is m = −di/do = −0.60/0.30 = −2, indicating the image is inverted and twice as large as the object. Therefore the image distance is 0.60 m.