Looking for classes? Ksquare Career Institute, Bengaluru →
A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point :
A
D
B
A
C
B
D
C
Detailed Solution
In a distance-time graph, the instantaneous speed at any instant is given by the slope of the curve at that instant: $v = \dfrac{ds}{dt}$.
So the instantaneous velocity is maximum where the curve is steepest.
Near A and B the curve is almost flat, so the slope (speed) is small.
Near D the curve flattens again, so the slope is small.
The curve rises most steeply around the point C, so the slope is maximum there.
Hence the maximum instantaneous velocity of the particle is around the point C.
So the instantaneous velocity is maximum where the curve is steepest.
Near A and B the curve is almost flat, so the slope (speed) is small.
Near D the curve flattens again, so the slope is small.
The curve rises most steeply around the point C, so the slope is maximum there.
Hence the maximum instantaneous velocity of the particle is around the point C.