Top fuel drag racer can reach the maximum speed of 304 mph at the end of the 1/4-mile (402 m) racetrack.
(a) Assuming that the acceleration is constant during the race, calculate the average value of the acceleration of the top fuel car.
(b) What is the ratio of that acceleration to the acceleration due to gravity?
To calculate the average acceleration of the top fuel drag racer, we need to use the equation of motion, which relates acceleration, initial velocity, final velocity, and displacement.
The equation is:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
In this case, the final velocity (v) is 304 mph, the initial velocity (u) is 0 mph since the car starts from rest, and the displacement (s) is the length of the racetrack, which is 402 m.
First, we need to convert the velocities from mph to m/s since the displacement is in meters. We can do this by multiplying the velocity by a conversion factor of 0.44704 m/s.
(a)
v = 304 mph * 0.44704 m/s = 136.49696 m/s
u = 0 mph * 0.44704 m/s = 0 m/s
Now we can use the equation of motion to solve for acceleration (a):
v^2 = u^2 + 2as
a = (v^2 - u^2) / (2s)
= (136.49696^2 - 0^2) / (2 * 402)
= 9282.3523 / 804
= 11.53835 m/s^2
Therefore, the average value of the acceleration of the top fuel car is approximately 11.54 m/s^2.
(b)
To find the ratio of the acceleration to the acceleration due to gravity, we need to compare the two values. The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Ratio = Acceleration / Acceleration due to gravity
= 11.54 m/s^2 / 9.8 m/s^2
= 1.18
Therefore, the ratio of the acceleration of the top fuel car to the acceleration due to gravity is approximately 1.18.