Final answer:
To determine the speed of the ball after being kicked, the work-energy principle is used, and it is found that the speed of the ball after moving 1.5 meters is 7.82 m/s.
Step-by-step explanation:
To find the speed of the ball after it has been kicked and moved 1.5 meters, we can use the work-energy principle.
The work done by the force is equal to the change in kinetic energy of the ball. The work W done by the force is the product of the force F and the distance d over which it acts:
W = F × d
The change in kinetic energy (ΔKE) is the difference between the final kinetic energy (KEf) and the initial kinetic energy (KEi), which is zero since the ball starts from rest:
ΔKE = KEf - KEi = KEf - 0
The final kinetic energy of the ball can be expressed as:
KEf = \(\frac{1}{2}mv^2\)
Thus, the work done is equal to the final kinetic energy:
W = \(\frac{1}{2}mv^2\)
To find the final speed v of the ball, we solve for v:
v = \(\sqrt{\frac{2W}{m}}\) = \(\sqrt{\frac{2Fd}{m}}\)
Plugging in the given values:
v = \(\sqrt{\frac{2 × 5.1 N × 1.5 m}{0.25 kg}}\)
= \(\sqrt{\frac{15.3}{0.25}}\)
= \(\sqrt{61.2}\) m/s
The final step is to calculate the result:
v = 7.82 m/s
Therefore, the speed of the ball after moving 1.5 meters is 7.82 m/s.