How to solve this question? I tried changing velocity to m/s and also tried changing acceleration to km/h^2 but i cannot get the answer still.

Question

A car is travelling at a velocity of $60km/h$. It then accelerates at $200m/s^2 $ for $2$ min. Calculate its final velocity? (Answer: 84km/h)

Answer 1

$v = v_0+at$

Yes, the units are all over the place, and working with a single set of units is probably best....But you should be able to convert units on the fly

$v = 60 \frac {km}{h} + (200 \frac m{s^2})(120 s)$

First an observation, $200 \frac {m}{s^2}$ is over $10$G's. That is our first clue that something has gone wrong...Anyway, assuming that it is correct and we are in fact talking about a rocket ship...

$v = 60 \frac {km}{h} + (24000 \frac m{s})$

Now we have some mismatched units...

$v = 60 \frac {km}{h} + (24000 \frac m{s})(\frac {1}{1000}\frac {km}{m})(3600 \frac sh)$

This will get everything into $\frac {km}{h}$

$v = 60 \frac {km}{h} + (24 \frac {km}{s})(3600 \frac sh)$

Now if the book answer is correct I see where this period of acceleration adds 24 units of speed to the equation. But these are the wrong units for this set-up

$v = 60 \frac {km}{h} + (86,400 \frac {km}{h})$

$v = 86,460 \frac {km}{h}$

So, what should our units have been?

$a = 200 \frac {m}{min^2}$ for 2 min is $(0.2 \frac {km}{min^2})(2\ min)(60 \frac {min}{h}) = 24 \frac {km}{h}$