Physics Help. Acceleration?

Question

Hi. I have been having trouble with acceleration in my physics class. Just wondering if someone can help me. Quite frankly i'm a bit dumbfounded.

The question is...

Calculate the instantanious speed in m/s at the 10 second mark for a car that accelerates at 2 m/s/s from a position of rest.

How do tou solve this? Any formulas to use?

Any help would greatly be appreciated.

Answer 1

a = acceleration.
v = velocity.
x = distance.

if x = f(t) then v = f'(t) and a = f''(t).

So if a = g(t) then v = the integral of g(t) + v0.
(don't know how to do the symbol thingy's)

Since g(t) is constant A. v(t) = A*t + v0.

Answer 2

2/m/s/s means that every second the car increases an
additional 2m/s. In other words, after 1 sec. the car has traveled
2m. The next second the car travels 4m/s.(4m). The next sec.
it travels 6m/sec(6m) and so on.
So the car traveled :
2m/sec+4m/sec+6m.sec+8m/sec+10m/sec+12m/sec+14m/sec+16m/sec+18m/sec+20m/sec.= 110m.
There is a formula to compute distance which you should find in
your book. See if you arrive at 110m.
To answer your question, 20m/sec. is the instantaneous speed
at the 10sec. mark and the car travelled 110m.
Good Luck.