A motorist is driving at a constant velocity of 28 m/s when he decides to pass a
car that is in front of him. He accelerates at a rate of 2.5 m/s2 for 3.0 seconds
while passing the car. What is his velocity at the end of the 3.0 seconds?
To find the final velocity of the motorist at the end of the 3.0 seconds, we can use the formula for acceleration:
vf = vi + at
Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time
The initial velocity of the motorist is given as 28 m/s, the acceleration is 2.5 m/s^2, and the time is 3.0 seconds.
Now, let's substitute these values into the formula:
vf = 28 m/s + (2.5 m/s^2)(3.0 s)
Calculating the acceleration term:
(2.5 m/s^2)(3.0 s) = 7.5 m/s
Now, substitute it back into the formula:
vf = 28 m/s + 7.5 m/s
Adding the velocities:
vf = 35.5 m/s
Therefore, the motorist's velocity at the end of the 3.0 seconds is 35.5 m/s.