A VW beetle goes from 0 to 53.0 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 53.0 mi/h in 0.700s. Find the acceleration (in m/s2) of the dragster.
(a) 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.
Given:
Initial velocity, u = 0 mi/h
Final velocity, v = 53.0 mi/h
Acceleration, a = 2.35 m/s^2
Since the initial and final velocities are given in mi/h, we need to convert them to m/s.
1 mi/h = 0.44704 m/s
Converting the velocities:
u = 0 mi/h = 0 m/s
v = 53.0 mi/h = 23.7117 m/s
We can now substitute these values into the equation and solve for t:
23.7117 = 0 + 2.35t
Rearranging the equation:
2.35t = 23.7117
Dividing both sides by 2.35:
t = 23.7117 / 2.35 = 10.1 s
Therefore, it takes 10.1 seconds for the Beetle to reach a speed of 53.0 mi/h.
(b) Again, we will use the equation v = u + at.
Given:
Initial velocity, u = 0 mi/h
Final velocity, v = 53.0 mi/h
Time, t = 0.700 s
Converting the velocities to m/s:
u = 0 mi/h = 0 m/s
v = 53.0 mi/h = 23.7117 m/s
Substituting the values and solving for acceleration, a:
23.7117 = 0 + a * 0.700
Simplifying the equation:
23.7117 = 0.7a
Dividing both sides by 0.7:
a = 23.7117 / 0.7 = 33.88 m/s^2
Therefore, the acceleration of the dragster is approximately 33.88 m/s^2.