Physics · Motion In A Straight Line · NEET
No. Average acceleration uses the total velocity change over the whole time interval, a_avg = Δv/Δt. Instantaneous acceleration is the value at one single instant, a = dv/dt (the limit of Δv/Δt as Δt goes to zero). They only give the same number when the acceleration is constant (uniform) throughout the motion.
Average acceleration is the slope of the straight line (chord) that joins the two end points (v1, t1) and (v2, t2). Instantaneous acceleration is the slope of the tangent line drawn at that one point on the curve. On a curved v-t graph these two slopes are different; on a straight-line v-t graph they are the same everywhere.
They are equal only for uniformly accelerated motion, where acceleration stays constant. In that case the v-t graph is a straight line, so the slope of the chord (average) equals the slope of the tangent (instantaneous) at every point. Free fall (a = g) is a common NEET example where both are equal to 9.8 m/s^2.
You cannot differentiate x with respect to t directly, so use the chain rule. First find dt/dx, then v = dx/dt = 1/(dt/dx). Then use a = v (dv/dx). This is the exact method NEET 2025 tested with t = x^2 + x. Do not just take the second derivative of x with respect to t blindly.
Yes. If the velocity at the start and the velocity at the end are equal (same magnitude and direction), then Δv = 0, so average acceleration = 0 over that interval, even though the instantaneous acceleration was non-zero at many points in between. A ball thrown up that returns to the hand with the same speed downward is a classic case.
The relation between time t and position x of a particle moving along a straight line is given by t = x^2 + x. The acceleration of the particle is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
a_avg = (v2 - v1)/(t2 - t1) = Δv/Δt, the change in velocity divided by the time interval. SI unit is m/s^2.
a = limit of (Δv/Δt) as Δt approaches zero = dv/dt. It is also equal to d^2x/dt^2 and to v(dv/dx).
Acceleration is a vector. It has both magnitude and direction, so it can be positive, negative or zero depending on the sign convention chosen.
NEET regularly gives velocity or position as an equation and asks for acceleration at an instant (as in 2025). Knowing average = chord slope and instantaneous = dv/dt (or v dv/dx) lets you solve these calculus-based kinematics problems quickly and avoid the second-derivative trap.
