A toy cart starts from rest and rolls down a long smooth ramp with a steady acceleration of 1.6…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A toy cart starts from rest and rolls down a long smooth ramp with a steady acceleration of $1.6\ \text{m/s}^2$ .

How far does it roll in the $8$ th second?
How far does it roll in the first $8$ seconds altogether?

Need a reminder? The key ideaShow

From rest with a steady acceleration $a$ , the distance in the $n$ th second is

\displaystyle s_n = \frac{a}{2}(2n - 1)

so successive seconds cover distances in the ratio $1 : 3 : 5 : 7 : \ldots$

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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