1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
monitta
3 years ago
6

The driver of a car moving at 90.0 km/h presses down on the brake as the car enters a circular curve of radius 195.0 m. If the s

peed of the car is decreasing at a rate of 4.0 km/h each second, what is the magnitude of the acceleration of the car (in m/s2) at the instant its speed is 58.0 km/h?
Physics
1 answer:
Olin [163]3 years ago
8 0

Answer:

Approximately \rm 1.73 \; \rm m \cdot s^{-2}.

Explanation:

The acceleration on the car comes in two parts:

  • The acceleration is due to the brakes is tangential to the circular curve.
  • The acceleration due to the circular motion of the car is centripetal. It points towards the center of the circle.

These two accelerations are perpendicular to each other.

Convert the current velocity to meters-per-second (\rm m \cdot s^{-1}.)

\begin{aligned} v &= 58.0\; \rm km \cdot h^{-1} \\ &= \left(58.0\; \rm km \cdot h^{-1}\left/\frac{3600\; \rm s}{1\; \rm h}\right.\right) \times \frac{1000\; \rm m}{1 \; \rm km} \\ &= \frac{58.0}{3600} \times 1000 \; \rm m \cdot s^{-1} \\ & \approx 16.1\; \rm m \cdot s^{-1}\end{aligned}.

Convert the acceleration due to braking to meters-per-second-squared (\rm m \cdot s^{-2}.)

\begin{aligned}a_{\text{tangential}} &= 4.0\; \rm km \cdot h^{-1} \cdot s^{-1} \\ &= \left(4.0\; \rm km \cdot h^{-1} \cdot s^{-1}\left/\frac{3600\; \rm s}{1\; \rm h}\right.\right) \times \frac{1000\; \rm m}{1 \; \rm km} \\ &= \frac{4.0}{3600} \times 1000 \; \rm m \cdot s^{-1} \cdot s^{-1} \\ & \approx 1.111111\; \rm m \cdot s^{-2} \end{aligned}.

Calculate the acceleration due to the circular motion:

\begin{aligned} a_\text{centripetal} &= \frac{v^2}{r} \\ &= \frac{\left(16.1\; \rm m \cdot s^{-1}\right)^2}{195.0\; \rm m} \\ & \approx 1.33112\; \rm m \cdot s^{-2}\end{aligned}.

Since the two accelerations are perpendicular to each other, the resultant acceleration can be found using the Pythagorean Theorem

\begin{aligned}a &= \sqrt{\left(a_\text{tangential}\right)^2 + \left(a_\text{centripetal}\right)^2} \\ &\approx \sqrt{1.111111^2 + 1.33112^2} \\ &\approx 1.73\; \rm m \cdot s^{-2}\end{aligned}.

You might be interested in
What law describes light
Darina [25.2K]

The law of reflection

6 0
3 years ago
Explain the following statement: A concentrated acid is not necessarily a strong acid.
andrezito [222]
Concentration involves the relative amounts of solvent and solute in a solution, when strength is related to the extent to which a substance dissociates :))
i hope this is helpful 
have a nice day 
3 0
3 years ago
Read 2 more answers
How do u do 5? Show me plz
nikitadnepr [17]
Solve the equation.it is hard to see
6 0
3 years ago
Debris from the solar system strikes the Earth as which of the following​
gogolik [260]

Answer: Meteors

Explanation:

7 0
3 years ago
¿Por qué en algunas partes el agua tiene mayor presión?
Phantasy [73]
Cuando la presión aumenta en el agua, disminuye el punto de fusión del hielo. Ósea esta a temperatura muy alta.


Espero que esto te ayude y no me haya confundido
7 0
2 years ago
Other questions:
  • You throw a 20-n rock vertically into the air from ground level. you observe that when it is a height 16.0 m above the ground, i
    15·1 answer
  • To simulate deafness, put ear plugs or cotton balls into your ears and put your hands over your ears to block out all sound. Des
    8·1 answer
  • You observe a distant galaxy. You find that a spectral line of hydrogen that is shifted from its normal location in the visible
    9·1 answer
  • Which years had the least sunspot activity?
    13·1 answer
  • A block and a ball have the same mass and move with the same initial velocity across a floor and then encounter identical ramps.
    15·1 answer
  • A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s average speed in miles per hour?
    5·1 answer
  • The specific heat capacity of oxygen is 918j/kg c. That means that it takes 918 J of energy to raise ____ kg of oxygen by 1 degr
    8·1 answer
  • Which two statements are true of electromagnetic waves?
    12·2 answers
  • What do alcohol, drugs, and tobacco all have in common?
    15·1 answer
  • The graph describes the motion of an object.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!