चित्र में किसी नियत (स्थिर) दिशा के अनुदिश चल रहे कण का चाल-समय ग्राफ दिखाया गया है । इसमें तीन समान समय अंतराल दिखाए गए हैं । किस अंतराल में औसत त्वरण का परिमाण अधिकतम होगा ? किस अंतराल में औसत चाल अधिकतम होगी ? धनात्मक दिशा को गति की स्थिर दिशा चुनते हुए तीनों अंतरालों में $v$ तथा $a$ के चिह बताइए । $A.B .C.$ व $D$ बिंदुओं पर त्वरण क्या होंगे ?

Average acceleration is greatest in interval 2 Average speed is greatest in interval 3 v is positive in intervals $1,2,$ and $3 a$ is positive in intervals 1 and 3 and negative in interval $2 a=0$ at $A, B, C, D$

Acceleration is given by the slope of the speed-time graph. In the given case, it is given by the slope of the speed-time graph within the given interval of time. since the slope of the given speed-time graph is maximum in interval $2,$ average acceleration will be the greatest in this interval.

Height of the curve from the time-axis gives the average speed of the particle. It is clear that the height is the greatest in interval $3 .$ Hence, average speed of the particle is the greatest in interval $3$

In interval 1:

The slope of the speed-time graph is positive. Hence, acceleration is positive. Similarly, the speed of the particle is positive in this interval.

In interval 2:

The slope of the speed-time graph is negative. Hence, acceleration is negative in this interval. However, speed is positive because it is a scalar quantity.

In interval 3:

The slope of the speed-time graph is zero. Hence, acceleration is zero in this interval. However, here the particle acquires some uniform speed. It is positive in this interval. Points $A, B, C,$ and $D$ are all parallel to the time-axis. Hence, the slope is zero at these points. Therefore, at points $A , B , C ,$ and $D ,$ acceleration of the particle is zero.