COULD ANYONE EXPLAIN DEAILED

WHAT IS AVG SPEEED

AND INSTANTANEOUS SPEED?

I DDNT GET THE IDEA OF CURVE BEING TANGENT!!!

Average Speed can be defined as the total distance travelled in the time interval.Im gonna explain u with the help of figure :

Average speed is the total distance travelled in the time interval.I m gonna explain u with u the help of figure:

Here, the particle is at point A at time(T₁) and at time (T₂), the particle is at point B,the distance travelled in time interval (T₁ toT₂) is 's'.So,the average speed of the particle is :-

Avg. speed=s/T₂-T₁ 

Instantaneous Speed is the distance travelled by the particle at any particular instant.We can explain it by plotting distance-time graph:

Here we can see that the slope of the triangle ACD makes a chord to the curve and as we know that the slope of the distance time graph gives us the speed.Now we come to the problem ,the slope of the triangle ACD will also give the speed but it will be different form the actual speed because it is not following the actual path of motion.

Speed=delta y/delta x

        =change in y / change in x

Now, when we will make delta x smaller and smaller ,the distance coverd in the time interval (X₁ to X₁+deltaX) will also decrease .Ultimately at a point the slope of the triangle ACD will become tangent to the curveand we will get the speed of the particle at that instant i.e. we will get instantaneous speed.

Instantaneous Speed= lim_{(deltax----->0)} delta y/delta x

                             =dy/dx

Now,that means we have to find the diffrential of the distance covered with respect to the time:

Speed_Ins.=ds/dt