Final answer:
To find the final velocity, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. We can also use the equation s = ut + 0.5at², where s is the distance traveled. By substituting the given values and solving the equations, we find that the velocity after traveling a distance of 24m is 12 m/s.
Step-by-step explanation:
To find the velocity of a body that accelerates uniformly from rest, we can use the equation:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (which is 0 in this case)
- a is the acceleration
- t is the time
In this case, the acceleration is 3 m/s² and the time is not given. However, we are given the distance traveled, which is 24m. We can use the equation:
s = ut + 0.5at²
where:
- s is the distance traveled
- u is the initial velocity (which is 0 in this case)
- a is the acceleration
- t is the time
Substituting the given values into the equation, we have:
24 = 0 + 0.5 * 3 * t²
Simplifying the equation:
24 = 1.5t²
Dividing both sides of the equation by 1.5, we get:
t² = 16
Taking the square root of both sides, we get:
t = 4 seconds
Now, we can substitute the time into the first equation to find the final velocity:
v = 0 + 3 * 4
v = 12 m/s
Therefore, the correct answer is A) 12 m/s.