A VW Beetle goes from 0 to 46.0 mi/h with an acceleration of +2.35 m/s2. (a) How much time does it take for the Beetle to reach this speed? (b) A top-fuel dragster can go from 0 to 46.0 mi/h in 0.750 s. Find the acceleration (in m/s2) of the dragster.
To solve this problem, we will use the equations of motion. The first equation relates the final velocity (v), initial velocity (u), acceleration (a), and time (t):
v = u + at
(a) To find the time it takes for the Beetle to reach a speed of 46.0 mi/h, we need to convert the velocity to m/s:
46.0 mi/h * (1609.34 m/1 mi) * (1 h/3600 s) = 20.57 m/s
Now we can use the equation to solve for time. The initial velocity (u) is 0, and the acceleration (a) is +2.35 m/s²:
20.57 m/s = 0 + 2.35 m/s² * t
Rearranging the equation to solve for time (t):
t = 20.57 m/s / 2.35 m/s² = 8.768 s
Therefore, it takes approximately 8.768 seconds for the Beetle to reach a speed of 46.0 mi/h.
(b) To find the acceleration of the dragster, we can rearrange the equation to solve for acceleration (a):
v = u + at
Rearranging to solve for acceleration (a):
a = (v - u) / t
The initial velocity (u) is 0, the final velocity (v) is 46.0 mi/h, and the time (t) is 0.750 s:
a = (46.0 mi/h * (1609.34 m/1 mi) * (1 h/3600 s) - 0) / 0.750 s
Simplifying the equation:
a = (20.57 m/s) / 0.750 s = 27.43 m/s²
Therefore, the acceleration of the dragster is approximately 27.43 m/s².
To solve part (a), we need to find the time it takes for the VW Beetle to reach a speed of 46.0 mi/h (which we'll convert to m/s later). We are given the acceleration of the Beetle as +2.35 m/s^2. We can use the following equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time taken
In this case, the initial velocity (u) is 0 (since it starts from rest), the final velocity (v) is 46.0 mi/h, and the acceleration (a) is +2.35 m/s^2. Let's convert the final velocity from mi/h to m/s:
1 mi/h = 0.44704 m/s
So, 46.0 mi/h = 46.0 * 0.44704 m/s = 20.51584 m/s
Now, let's solve for time (t):
20.51584 = 0 + 2.35 * t
20.51584 = 2.35t
Dividing both sides by 2.35:
t = 20.51584 / 2.35
t ≈ 8.72 s
Therefore, it takes approximately 8.72 seconds for the VW Beetle to reach a speed of 46.0 mi/h.
Moving on to part (b), we need to find the acceleration of the dragster. We are given the time taken as 0.750 s, and the final velocity as 46.0 mi/h. We'll again convert the velocity to m/s:
46.0 mi/h = 46.0 * 0.44704 m/s = 20.51584 m/s
Now, we can use the equation of motion from above to find the acceleration:
20.51584 = 0 + a * 0.750
20.51584 = 0.75a
Dividing both sides by 0.75:
a = 20.51584 / 0.75
a ≈ 27.35 m/s^2
Therefore, the acceleration of the dragster is approximately 27.35 m/s^2.
46 mi/hr = 20.56 m/s
so v = at means t = 20.56/2.35 s
work the other similarly
or, just consider the ratio of time lengths