Question

A small marble is rolling down on an incline. The marble was released from rest when the timer was started. The distance travelled by the marble as the function of time is shown in the figure.

100 90 80 70 60 음음 ' , 50 40 30 20 10 0 0 2 3 4 5 6 7 8 9 10 t (s)

What is the acceleration of the marble? Please, note that the curve passes through at least one grid intersection point.

Answer 1

From the graph you can see that

The graph between the distance and the time is non linear

And it's look like parabola

Now the standard equation of parabola passing from the origin can be written as

$X^2=ky$

Now here X=t(time)

y=d=distance

And k = constant

Therefore the equation of the graph can be written as

$t^2=kd$. ..........(1)

Now to find the k put the initial condition from the graph

i.e

at

t= 5. d= 90

Put this values in equation (1)

$5^2=k*90$

K= 25/90

K=0.277

Hence the equation becomes

$t^2=0.277d$

$d=t^2/0.277$

Now differentiate above equation with respect to time (t)

You will get velocity i.e

$V=d(d)/dt$

V= 2t/0.277

And if you differentiate velocity with respect to time (t) then you will get acceleration (a)

acceleration (a)=d(V)/dt

a=2/0.277= 7.2202 cm/sec^2

Hence the acceleration a=7.2202 cm/sec^2

You can also write acceleration a= 0.072202 m/sec^2