How to find average of any Case with using integration ? such as a particle is moving in x axis. At any instant of time the equation of position of the particle is X= a+bt2, where a=6m and b=3.5 m/s2, if t is in second then find the average speed of the particle between t= 3 to 6 second using the method of integration

Open in App

Solution

given X =A +BT^2

dX/dT = V =2BT

dV/dT = a (ACCELERATION) = 2B

we know definite integral of acceleration gives the average velocity

pls, refer the image... view image on a computer for clarity

Suggest Corrections

Similar questions

Q. Position -time(x-t) grapg of a particle moving along x-axis is as shown in the figure.The average speed of particle in time interval t=0 to t=10s is

Q. The position of a particle along along x-axis is given by

x = a + b t^{2}

, where a= 8.5 m, b = 2.5 m and

t

is in seconds. What is its average velocity at t = 2.0 s? What will be its average velocity between

t = 2 s

t = 4 s

Q. A particle moves along a straight line. Its position at any instant is given by

x = 32 t - \frac{8 t^{3}}{3}

where

x

is in metre and

t

in second. Find the acceleration of the particle at the instant when particle is at rest.

Position-time (x-t ) graph of a particle moving along x-axis is as shown in the figure.The average speed of particle in time interval t=0 to t=10 s is?

Q. The position of a particle moving along x-axis is given by

x = (5 t^{2} - 4 t + 20) m

, where

t

is in second. Find the magnitude average velocity between

1 s

and

3 s

Join BYJU'S Learning Program

given X =A +BT^2 dX/dT = V =2BT dV/dT = a (ACCELERATION) = 2B we know definite integral of acceleration gives the average velocity pls, refer the image... view image on a computer for clarity

given X =A +BT^2

dX/dT = V =2BT

dV/dT = a (ACCELERATION) = 2B

we know definite integral of acceleration gives the average velocity

pls, refer the image... view image on a computer for clarity