A car is moving at 10 m/s when it begins to be accelerated at 2.5m/s2. how long does the car take to reach a speed of 25 m/s? How far does it go during this period?

vf=vi+at solve for time

how far? average velocity= (10+25)/2

distance=averagevelocity*time

To find the time it takes for the car to reach a speed of 25 m/s, you can use the formula:

v = u + at

Where:
v = final velocity (25 m/s)
u = initial velocity (10 m/s)
a = acceleration (2.5 m/s^2)
t = time

Rearranging the formula, we have:

t = (v - u) / a

Substituting the given values:

t = (25 - 10) / 2.5
t = 15 / 2.5
t = 6 seconds

So it takes the car 6 seconds to reach a speed of 25 m/s.

To find the distance the car travels during this time, you can use the formula:

s = ut + (1/2)at^2

Where:
s = distance
u = initial velocity (10 m/s)
t = time (6 seconds)
a = acceleration (2.5 m/s^2)

Substituting the values:

s = 10 * 6 + (1/2) * 2.5 * 6^2
s = 60 + (1/2) * 2.5 * 36
s = 60 + 18 * 2.5
s = 60 + 45
s = 105 meters

Therefore, the car travels a distance of 105 meters during the time it takes to reach a speed of 25 m/s.