A car uniformly accelerates from 0 to 27.0 m/s. A 68.0-kg passenger experiences a horizontal force of 390.0 N.
1)How much time does it take for the car to reach 27.0 m/s? (Express your answer to three significant figures.)
My teacher didn't explain how we could ever find the time it takes without having distance so I'm lost.
Vf=vi+at where a= force/mass
solve for time.
fd=1/2mv^2: 390d=0.5*68*27^2 d=68.6 68.6=27^2-0/2a a=5.31m/s^2
Well, I guess you could try tracking down the distance using a really good detective. Maybe ask Sherlock Holmes, he's great at solving mysteries. But if you want a more scientific answer, you could use the formula for acceleration to figure out the time it takes. The formula is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. Since you are given the acceleration, final velocity, and the fact that the initial velocity is 0, you can rearrange the formula to solve for time. Give it a shot, and remember, even if you don't find all the answers, you're still one step closer to becoming a detective like Sherlock Holmes. Good luck!
To find the time it takes for the car to reach 27.0 m/s, we can use the equation of motion that relates acceleration (a), time (t), and final velocity (vf) to initial velocity (vi):
vf = vi + at
In this case, the car starts from rest (vi = 0), accelerates uniformly, and reaches a final velocity of 27.0 m/s (vf = 27.0 m/s).
Given that the car accelerates uniformly, we can assume that the force experienced by the passenger is the net force acting on the passenger. The force (F) is related to mass (m) and acceleration (a) by Newton's second law:
F = ma
Rearranging the equation to solve for acceleration (a):
a = F/m
Now we can substitute the given values into the equation:
a = 390.0 N / 68.0 kg
a ≈ 5.735 m/s² (rounded to three significant figures)
Now we can substitute the known values into the first equation to solve for time (t):
27.0 m/s = 0 + (5.735 m/s²) * t
Simplifying the equation:
27.0 = 5.735t
Divide both sides of the equation by 5.735:
t = 27.0 / 5.735
Calculating the result:
t ≈ 4.71 s (rounded to three significant figures)
Therefore, it takes approximately 4.71 seconds for the car to reach a velocity of 27.0 m/s.