Final answer:
The final speed of the jet car is approximately 98 m/s, and the acceleration is approximately 18.843 m/s² when it travels 0.25 mile in 5.2 seconds.
Step-by-step explanation:
To determine the jet car's final speed and acceleration, we need to convert the distance from miles to meters and then use the kinematic equations for uniformly accelerated motion. A quarter mile is equivalent to 402.336 meters (1 mile = 1609.34 meters). Assuming the car starts from rest and accelerates evenly, we can use the equation:
v = u + at,
where v is the final velocity, u is the initial velocity (0 m/s since it starts from rest), a is the acceleration, and t is the time (5.2 seconds). Since the car starts from rest, the equation simplifies to v = at. Next, we use the distance equation:
s = ut + (0.5)at2,
where s is the distance (402.336 meters), which again simplifies to s = (0.5)at2 since u=0. By rearranging to solve for a, we have:
a = (2s)/t2 = (2 * 402.336)/(5.2)2 ≈ 18.843 m/s2.
Now we can find v using a and t:
v = at = 18.843 * 5.2 ≈ 98 m/s.
Therefore, the final speed of the jet car is approximately 98 m/s, and the acceleration is approximately 18.843 m/s2.