Physics · Laws Of Motion · NEET
F = dp/dt is the general and more fundamental form. F = ma is a special case that we get ONLY when the mass m stays constant. Starting from F = dp/dt with p = mv: if m is constant, F = m(dv/dt) = ma. For NEET, use F = ma for normal blocks and cars (constant mass), but remember that for rockets losing fuel, the mass changes, so you must go back to F = dp/dt. NEET has asked which form is more general — the answer is dp/dt.
NCERT builds F = ma from experiments on momentum because force is really defined by how fast momentum changes, not by mass and acceleration separately. The observations show: the same force for the same time gives the same change in momentum to any body. Writing this as F is proportional to dp/dt, and choosing the SI unit so the constant of proportionality is 1, gives F = dp/dt = ma. This is why momentum is called 'basic to the effect of force on motion'.
No. F = ma assumes constant mass. If mass changes with time (a rocket ejecting gas, a conveyor loading sand), you cannot pull m out of the derivative. You must use the full form F = dp/dt = d(mv)/dt. For every ordinary NEET block, wedge, or car problem the mass is constant, so F = ma is safe there.
From F = ma, one newton is the force that gives a mass of 1 kg an acceleration of 1 m/s squared. So 1 N = 1 kg x 1 m/s^2 = 1 kg m/s^2. This definition comes straight from the second law and is why the SI proportionality constant is exactly 1.
It is always the NET (resultant) external force. If several forces act, first add them as vectors to get one resultant F, then use F = ma. This is why NEET problems with two perpendicular forces first ask you to find the resultant (using the square root of the sum of squares), and only then divide by mass to get acceleration.
Because F = ma is a vector equation and m is a positive scalar. Multiplying the acceleration vector by a positive number cannot change its direction. So acceleration points exactly along the net force, whatever the direction of velocity. A body can move north while accelerating east if the net force points east.
The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it are, respectively:
A block of mass m is placed on a smooth inclined wedge ABC of inclination theta. The wedge is given a horizontal acceleration 'a' towards the right. The relation between a and theta for the block to remain stationary on the wedge is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The net external force on a body equals the rate of change of its momentum, F = dp/dt, which becomes F = ma when the mass is constant.
The newton (N). One newton is the force that gives 1 kg an acceleration of 1 m/s^2, so 1 N = 1 kg m/s^2.
It is a vector equation. Force and acceleration are vectors in the same direction, while mass is a positive scalar.
The first law is a special case of the second: when the net force F = 0, acceleration a = 0, so the body stays at rest or moves with constant velocity.
From a = F/m, acceleration is inversely proportional to mass. For the same net force, a larger mass gives a smaller acceleration.
