constant acceleration

[red and white kop!]

if a ball is placed on a straight sloping track and then released from rest, the distances that it moves in successive equal intervals of time are found to be in the ratio 1:3:5:7...
show that this is consistent with the theory that the ball rolls down the track with constant acceleration

what is the best way to do this? personnally i would try to prove that the accelerations over the four periods of time considered are equal, but is this appropriate? would it be useful to compare these to acceleration over the total distance considered 16D? or could one use analytical geometry (a=gradient)?

 

[Deleted member 4993]

if a ball is placed on a straight sloping track and then released from rest, the distances that it moves in successive equal intervals of time are found to be in the ratio 1:3:5:7...
show that this is consistent with the theory that the ball rolls down the track with constant acceleration

what is the best way to do this? personnally i would try to prove that the accelerations over the four periods of time considered are equal, but is this appropriate? would it be useful to compare these to acceleration over the total distance considered 16D? or could one use analytical geometry (a=gradient)?

Make a chart:

time                        Position
  0                               0
  t                               d
 2t                               4d
 3t                               9d
 4t                              16d

Now you can take several paths to answer. My favorite path wiuld be to investigate average speed in that time interval.

 

[red and white kop!]

please continue.
but could it be done like how i suggested, caulculating accelration over each interval?

 

[Deleted member 4993]

please continue.
but could it be done like how i suggested, caulculating accelration over each interval?

yes - that is the principle

time                   position                           average velocity                 average acceleration

0                          0
t                          d                                   d/t
2t                        4d                                  3d/t                              2d/t^2
3t                        9d                                  5d/t                              2d/t^2
4t                       16d                                  7d/t                              2d/t^2
.
.

 

[red and white kop!]

thanks