Lesson 3 of 9 · 10 min
Acceleration
NCERT § "Acceleration"
Two multi-flash photos of the same car, one second apart each. In one the gaps grow, in the other they shrink. That growth and shrinkage is acceleration.
The lesson in notes
In short
Dividing the change in velocity by the time interval gives the average acceleration; the instantaneous acceleration is a = dv/dt = d²x/dt².
Acceleration is the slope of the velocity-time (v-t) graph at a given instant; SI unit m s⁻².
The sign of acceleration is fixed by the chosen positive direction. A body speeds up when v and a have the same sign and slows down when they have opposite signs.
A body can have zero velocity and non-zero acceleration at the same instant, for example at the highest point of a vertical throw.
With uniform (constant) acceleration, plotting v against t gives a straight line; for uniform motion (a = 0) that line runs parallel to the time axis.
The x-t graph curves upward when a > 0 and downward when a < 0; for a = 0 it is a straight line.
The area under the v-t graph over an interval equals the displacement in that interval, with area below the time axis counted as negative.