Physics · Motion In A Straight Line · NEET
List the five variables: u (initial velocity), v (final velocity), a (acceleration), t (time), s (displacement). In a problem you are given three of them and asked for a fourth. One variable is neither given nor asked — the equation that does NOT contain that missing variable is the one to use. v = u + at has no s. s = ut + ½at² has no v. v² = u² + 2as has no t. So the missing variable directly points to the formula.
Use v² = u² + 2as. This is the only equation of the three that has no t (time) in it. So whenever a problem gives you velocities and distance but says nothing about time, and does not ask for time, go straight to v² = u² + 2as. Example: a bullet slowing inside wood — you know u, final speed and distance, no time, so v² = u² + 2as.
Use s = ut + ½at². This equation contains u, a, t and s but not v. So if a question gives you time and asks for distance (or gives distance and asks time), and final velocity never appears, this is your equation. Free-fall drop problems (find how far it falls in t seconds) usually use this one.
Use v = u + at when the problem is only about velocities, acceleration and time, and displacement s is not involved. For example: 'a car speeds up from 10 m/s at 2 m/s² for 5 s, find its final speed.' Here s is the missing variable, so use v = u + at. It is the only equation without s.
You can still use these equations — a is just one of the five variables. If a is unknown but you know the other four relationships, choose the equation that lets you solve for a. Very often v² = u² + 2as is rearranged to a = (v² − u²)/(2s) when time is not given, or v = u + at gives a = (v − u)/t when time is given.
Yes. The three equations only work for uniform (constant) acceleration. If the problem gives velocity or position as a function of time (like x = At + Bt² or v = At + Bt²), the acceleration is not constant, so you must differentiate or integrate: v = dx/dt, a = dv/dt, and s = ∫v dt. NEET regularly tests this — spotting that acceleration is not constant is itself the first decision.
A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is (g = 10 m/s²):
A bullet enters a wooden block with speed u and, after travelling 24 cm inside it, its speed reduces to u/3. Assuming uniform retardation, the further distance it travels before coming to rest is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. Free fall is just uniform acceleration with a = g (about 9.8 or 10 m/s²). Use the same three equations, being careful with the sign convention: take one direction as positive and keep u, v, a and s consistent with it.
u (initial velocity), v (final velocity), a (acceleration), t (time), and s (displacement). Write down which three you know and which one you want. The one left over — neither known nor wanted — tells you the equation.
It is the fastest when time is not involved, but it cannot find time and cannot be used if acceleration is not constant. Match the equation to what the problem gives; there is no single 'safe' formula for every case.
Pick a positive direction first. If up is positive, then g points down and a = −g for a ball going up or coming down. If down is positive (common for dropped objects), then a = +g. Keep every quantity consistent with that choice.
Whenever acceleration is not constant. If the question gives x(t) or v(t) as an equation (for example v = At + Bt²), differentiate for velocity/acceleration or integrate for displacement — the three formulas do not apply there.
