a driver starting from rest accelerates at a rate of 1.5m/s^2 for 20s until reaching a certain speed she then continues driving at this constant speed for an additional 20s what maximum speed does the driver attain what total distance does the driver cover during the 40s that she is in motion

max speed:

v=at=1.5*20=30m/s
distance covered during acceleration:
d=1/2 a t^2=1/2*1.5*400=300m

constant speed: distance covered
d=30m/s*20s=600m

total distance=300+600=900m

To solve this problem, we need to break it down into two parts:

1. Finding the maximum speed attained by the driver
2. Finding the total distance covered by the driver

1. Finding the maximum speed attained by the driver:
We know that the driver starts from rest and accelerates at a rate of 1.5 m/s^2 for 20 seconds. We can use the equation of motion:

v = u + at

Where:
v = final velocity
u = initial velocity (which is 0 in this case, as the driver starts from rest)
a = acceleration
t = time

Plugging in the given values:
v = 0 + (1.5 m/s^2) * (20 s)
v = 30 m/s

Therefore, the maximum speed attained by the driver is 30 m/s.

2. Finding the total distance covered by the driver:
We know that the driver drives at a constant speed for an additional 20 seconds. Since the speed is constant, we can use the equation:

s = vt

Where:
s = distance
v = velocity (which is 30 m/s)
t = time (which is 20 s)

Plugging in the values:
s = (30 m/s) * (20 s)
s = 600 m

Therefore, the total distance covered by the driver during the 40 seconds that she is in motion is 600 meters.