Univ-Phys

One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 5.0m/s, they then have the same kinetic energy.

What were the original speeds of the two cars?

  1. 👍 0
  2. 👎 0
  3. 👁 3,418
  1. M1 is the heavier car and the mass of the other car is M2 = M1/2

    Orginally,
    (1/2) M1 V1^2 = (1/2)*(1/2)(M1/2)V2^2

    which implies that
    V1^2 = (1/4)V2^2
    V1 = V2/2

    Also,
    (1/2)M1*(V1+5)^2 = (1/2)(M1/2)(V2+5)^2
    = (1/2)(M1/2)(2V1 + 5)^2
    (V1+5)^2 = (1/2)(2V1+5)^2
    V1^2 + 10 V1 + 25 = 2V1^2 + 10 V1 + 25/2
    V1^2 = 25/2
    V1 = 5/sqrt2
    V2 = 5 sqrt2

    1. 👍 0
    2. 👎 4

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A car of mass m moving at a speed v1 collides and couples with the back of a truck of mass 3m moving initially in the same direction as the car at a lower speed v2. (Use any variable or symbol stated above as necessary.) (b) What

    asked by Joe on March 12, 2014
  2. Physics

    Two cars are moving. The first car has twice the mass of the second car, but only half as much kinetic energy. Then, both cars increase their speed by 8.00 m/s. They then have the same kinetic energy. The original speeds of the

    asked by Vladimyr on May 29, 2012
  3. science

    When a car's speed doubles from 20 m/s to 40 m/s, by how many times does the car's kinetic energy increase? Show your work. The mass of the car is 1000 kg. k=1/2mv^2

    asked by anonymos on June 10, 2020
  4. Physics

    A car of mass 120kg moving with a velocity of 30m/s overtake and collide with another car of mass 100kg moving with at 12m/s.After collision the two car separate with a relative velocity of 4m/s (1)calculate the velocity each car

    asked by Same on June 6, 2020
  5. Physics

    When four people with a combined mass of 320 kg sit down in a car, they find that the car drops 0.80 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the car's vibration if

    asked by Y0gi on December 7, 2010
  1. Physics

    A car is traveling at 14 m/s. How fast would the car need to go to double its kinetic energy? By what factor does the car's kinetic energy increase if its speed is doubled to 28 m/s? We only get 3 chances and I'm on my last one

    asked by falcon306 on August 8, 2011
  2. motion problem (please check)

    A 8000N car is traveling 12 m/s along a horizntal road when the brakes are applied. The car skids to a stop in 4.0s. How much kinetic energy does the car have. my work: W= 8000N/9.18m/s mass= 815.49 kg Kinetic energy=

    asked by Jenny on November 6, 2006
  3. physics

    A 2000 kg car is moving with a velocity of 50 km/hr. What is its kinetic energy? If the car reduces its speed by half, by what factor is the kinetic energy changed?

    asked by rosie on June 30, 2011
  4. physics

    several students are riding in bumper cars at an amusement park. the combined mass of a car A and its occupants is 250 kg. the combined mass of car B and its occupants is 200 kg. Car A is 15 m away from car B and moving to the

    asked by shelly on June 9, 2008
  5. physics

    Car A is travelling at 22.0 m/s and car B at 29.0 m/s. Car A is 300 m behind Car B when the drive of car A accelerates his car with an acceleration of2.4 m/s2. How long does it take Car A to overtake Car B?

    asked by shay on June 27, 2015

You can view more similar questions or ask a new question.