An object starts at 4 m/s and speeds up at a steady 2 m/s²…

Contributed by StemPy Lab

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

An object starts at $4\ \text{m/s}$ and speeds up at a steady $2\ \text{m/s}^2$ . Make a table of its velocity and distance from the start at every second from $t = 0$ to $t = 5\ \text{s}$ .

Need a reminder? The key ideaShow

For steady acceleration: $v = u + at$ , $s = ut + \tfrac12 at^2$ , $v^2 = u^2 + 2as$ , and $s = \tfrac12(u + v)t$ .

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.

Step 1. The rules. $v = 4\ \text{m/s} + 2\ \text{m/s}^2 \times t$ and $s = 4\ \text{m/s} \times t + \tfrac12 \times 2\ \text{m/s}^2 \times t^2$ .

Step 2. The table.

$t$ (s)	0	1	2	3	4	5
$v$ (m/s)	4	6	8	10	12	14
$s$ (m)	0	5	12	21	32	45

Answer: At $5\ \text{s}$ : $14\ \text{m/s}$ and $45\ \text{m}$ .

Check. The distance gained each second grows by $2\ \text{m}$ : $5, 7, 9, 11, 13$ .

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