Home
Class 11
PHYSICS
Suppose displacement y(t) (that is, y as...

Suppose displacement `y(t)` (that is, y as a function of t ) is given by
`y(t)=t^(3)`

Text Solution

Verified by Experts

Find velocity `(dy//dt)` at `t = 3 sec`.
Displacement at `t+Deltat` is
`y(t+Deltat)=(t+Deltat)^(3)`
`=(t^(3)+3t^(2)Deltat+3t Deltat^(2)+Deltat^(3))`
hence displacement from t to `t+Deltat` is `Deltay`
`Deltay=y(t+Deltat)-y(t)=(3t^(2)Deltat+3tDeltat^(2)+Deltat^(3))`
Substituting this into Equation (i) gives
`(dy)/(dt)=underset(Deltararr0)(lim)(Deltay)/(Deltat)=underset(Deltatrarr0)(lim)[3t^(2)+3tDeltat+Deltat^(2)]`
Here we can see that if we take very small value of `Deltat` then value of `dy//dt` will approach `3t^(2)` as all other terms will become negligible and impossible to measure by any instrument available in this world.
hence, `" " (dy)/(dt)=3t^(2) rArr (dy)/(dt)=v(at " " t =3sec)=3(3)^(2)=27 m//s`
Promotional Banner

Topper's Solved these Questions

  • UNIT DIMENSION, VECTOR & BASIC MATHS

    BANSAL|Exercise Solved Example|17 Videos

  • UNIT DIMENSION, VECTOR & BASIC MATHS

    BANSAL|Exercise PRACTICE EXERCISE|4 Videos

  • KINETIC THEORY OF GASES

    BANSAL|Exercise Section-B|13 Videos

Similar Questions

Explore conceptually related problems

A wave pulse is travelling on a string at 2 m/s. displacement y of the particle at x = 0 at any time t is given by y=2/(t^2+1) Find (i) Expression of the function y = (x, t) i.e., displacement of a particle position x and time t.

Suppose that the position function for a particle is given as ⃗ r(t)=x(t)ˆi+y(t)ˆj with x(t)=t+1 and y(t)=(t^(2)/8)+1) The ratio of magnitude of average velocity (during time interval t=2 to 4sec) to the speed at t=2sec is

If the position of a particle along Y axis is represented as a funtion of time t by the equation y(t)=t^(3) then find displacement of the particle during the period t to t+Deltat

The displacement function of a S.H.M is given by y = cos [(omega t + phi)] if at t = 0 th displaxcement is y = 1 on and velocity cm s^(-1) The value amplitude (A in cm) is

The displacement of a particle executing SHM is given by Y=5 " sin "(4t+(pi)/(3)) If T is the time period and the mass of the particle is 2g, the kinetic energy of the particle When t= (T)/(4) is given by-

The displacement y of a particle periodic motion is given by y = 4 cos ((1)/(2) t) sin (1000 t) This expression may be considered as a result of the superposition of

The horizontal and vertical displacements x and y of a projectile at a given time t are given by x= 6 "t" and y= 8t -5t^2 meter.The range of the projectile in metre is:

If y is displacement and t is time, unit of (d^(2)y)/(dt^(2)) will be

The displacement of a particle executing S.H.M. is given by y = 10 sin [6t + (pi)/(3)] where y is in metres and t is in seconds. Then the initial displacement and velocity of the particle is