Answer:

We can use the kinematic equation:

v^2 = u^2 + 2as

where:

v = final velocity = u + at (since the initial velocity u is zero)

a = acceleration = 12 m/s^2

s = distance travelled

t = time taken

Plugging in the given values, we get:

(15 m/s)^2 = 0 + 2(12 m/s^2)s

225 m^2/s^2 = 24s^2

s^2 = 9.375 m^2

s = 3.06 m (rounded to two decimal places)

Now, we can use another kinematic equation:

v = u + at

where:

u = initial velocity = 0

a = 12 m/s^2

t = time taken = ?

Plugging in the given values, we get:

15 m/s = 0 + 12 m/s^2(t)

t = 1.25 seconds

Therefore, the drag racer accelerated for 1.25 seconds at 12 m/s^2 in order to increase their velocity by 15 m/s.