Question

If a car has an initial velocity of 103m/s and accelerates at 1m/s for 3 seconds, what will its final velocity be? Can you please show me how to work this question out with math answers and explain it to me. Thank you.

Answer 1

We start counting when it's moving 103m/s. (And incidentally, that's pretty fast for a car. Formula 1, maybe?)

Each second after that, it moves 1m/s faster than it was before.

So if we call time by seconds, as we often do in these things, we call the start, after zero seconds, t0.

t0 = 103 m/s

After one second, it's moving 1m/s faster:

t1 = 104 m/s

The next second, 1m/s faster again...

t2 = 105 m/s

and finally...

t3 = 106 m/s

In general, after n seconds, it's moving at (103 + n) m/s.

It's actually accelerating at 1 m/s^2, or "one meter per second per second" since it gets 1 meter per second faster every second.

Answer 2

I used a shorthand that was wrong in this question, and it might confuse you.

When I say

t0 = 103 m/s

what I should have said, to be clear, was

speed at t0 = 103 m/s

and so on.