Obtain equations of motion for constant ...

Obtain equations of motion for constant acceleration using method of calculus.

Text Solution

Verified by Experts

By definition `a=(dupsilon)/(dt)`
`dupsilon=a" "dt`
Integrating both sides
`int_(upsilon_(0))^(upsilon)dupsilon=int_(0)^(t)a" "dt`
`" "=aint_(0)^(t)dt" (a is constant)"`
`upsilon-upsilon_(0)=at`
`" "upsilon=upsilon_(0)+at`
Further, `upsilon=(dx)/(dt)`
`" "dx=upsilon" "dt`
Integrating both sides
`int_(x_(0))^(x)dx=int_(0)^(t)upsilondt`
`" "=int_(0)^(t)(upsilon_(0)+at)dt`
`x-x_(0)=upsilon_(0)t+1/2a" "t^(2)`
`x=x_(0)+upsilon_(0)t+1/2a" "t^(2)`
We can write
`a=(dupsilon)/(dt)=(dupsilon)/(dx)(dx)/(dt)=upsilon(dupsilon)/(dx)`
Or, `upsilondupsilon=a" "dx`
Integrating both sides,
`int_(upsilon_(0))^(upsilon) upsilondv=int_(x_(0))^(x)adx`
`(upsilon^(2)-upsilon_(0)^(2))/2=a(x-x_(0))`
`upsilon^(2)=upsilon_(0)""^(2)+2a(x-x_(0))`
`" "`The advantage of this method is that it can be used for motion with non-uniform acceleration also.
Now, we shall use these equations to some important cases.

(A) : The equations of motion in scalar form can be applied only if acceleration and velocity are along the same line. ( R) : If the acceleration of a body is constant then its motion is known as uniform motion.

Both (A) and ( R) are ture and ( R) is the correct explanation of (A)

Both (A) and ( R) are true and ( R) is not the correct explanation of (A)

(A) is true but ( R) is false

Both (A) and ( R) are false

(A): The equations of motion in scalar form can be applied only if acceleration and velocity are along the same line. (R): If the acceleration of a body is constant then its motion is known as uniform motion.

Both (A) and (R) are true and (R) is the correct explanation of (A)

Both (A) and (R) are true and (R) is not the correct explanation of (A)

(A) is true but (R) is false

Both (A) and (R) are fals

A particle moving with a constant acceleration describes in the last second of its motion 9//25^(th) of the whole distance .If it starts from rest,how long us the particle in motion and through what distance does it moves if it describes 6 cm in the first sec.?

5s, 150 cm

10s,150 cm

15s,100cm

None

Obtain equations of motion for constant acceleration using method of calculus.

Text Solution

Similar Questions

Knowledge Check

(A) : The equations of motion in scalar form can be applied only if acceleration and velocity are along the same line. ( R) : If the acceleration of a body is constant then its motion is known as uniform motion.

(A): The equations of motion in scalar form can be applied only if acceleration and velocity are along the same line. (R): If the acceleration of a body is constant then its motion is known as uniform motion.

A particle moving with a constant acceleration describes in the last second of its motion 9//25^(th) of the whole distance .If it starts from rest,how long us the particle in motion and through what distance does it moves if it describes 6 cm in the first sec.?

Similar Questions

Recommended Questions