Theory q on uniformly accelerated motion?

Question

a particle starts from rest and travels in a straight line for 4s. if the particle is accelerating at a constant rate, which of the following could be the distances traveled by the particle during each consecutive second?

a. 10m, 20m, 30m, 40m

b. 5m, 15m, 25m, 35m

c. 5m, 25m, 125m, 625m

d. 2m, 4m, 8m, 16m

i have no idea how to go about this question, so if anyone could help me i'd be most appreciative.

Answer 1

A.  It's the only linear series.

C and D are exponential.  B is just weird.

Although, technically, a particle can never truly be at rest.

Answer 2

You know that s=ut+1/2at^2.  Putting in t=1,2 with the corresponding distances (ADDED) will give u and a.  You can then check against the next two distances.

Example (I will do a. and leave the rest to you):

First distance gives 10=u*1+1/2a*1^2 = u+a/2

Second gives 30=2u+2a (note I added the first two distances here).

Solving gives a=10, u=5.

To check against the next two distances (the 30m and 40m figures) we calculate s:

s=5t+5t^2

With t=3, s=60m, so the distance in the third second is 60-20-10=30m.  This checks out with the data given.

With t=4, s=100m, so the fourth second distance is 40m as also expected.  We conclude that (a) is possible.  If the distances we calculate are not those given in the question, then the data are not possible with uniform acceleration.