- #1

Drill

- 7

- 0

Hi everybody

we know that if we have an object sliding on a frictionless ramp,

the acceleration force will be constant, and it equals to

a=g * sin(theta)

where theta is the ramp angle w.r.t. the ground

so the path of motion in this problem can be written mathematically as a linear function

y(x)=bx

and hence the tangent tan(theta)= bx /x =b

The Question is

if the path of motion is parabolic and is of the form

y(x) = a x^2

how to solve for the acceleration with respect to time ??

be aware that ,in this case the acceleration is not constant , and it always equals to the tangent of the parabola at the current location of the object.

and the tangent in this case is the first derivative of y which is

y'=2ax

as we see the tangent and hence the acceleration is a function of x

so ,

how to calculate the time as the function of position ??

thanks

we know that if we have an object sliding on a frictionless ramp,

the acceleration force will be constant, and it equals to

a=g * sin(theta)

where theta is the ramp angle w.r.t. the ground

so the path of motion in this problem can be written mathematically as a linear function

y(x)=bx

and hence the tangent tan(theta)= bx /x =b

The Question is

if the path of motion is parabolic and is of the form

y(x) = a x^2

how to solve for the acceleration with respect to time ??

be aware that ,in this case the acceleration is not constant , and it always equals to the tangent of the parabola at the current location of the object.

and the tangent in this case is the first derivative of y which is

y'=2ax

as we see the tangent and hence the acceleration is a function of x

so ,

how to calculate the time as the function of position ??

thanks

Last edited: