We read your photo as:

Determine the acceleration of the truck in terms of a.

Physics

ScanSolve AI Answer

Answer

mcarmtrucka\text{}\frac{m_{car}}{m_{truck}} a\text{}

car driver\text{car driver}\text{}

Step-by-step solution

2 steps
  1. Determine the acceleration of the truck in terms of aa.

    Let mcarm_{car} be the mass of the car and mtruckm_{truck} be the mass of the truck.
    Let acara_{car} be the acceleration of the car and atrucka_{truck} be the acceleration of the truck.
    Assume aa refers to the acceleration of the car, so acar=aa_{car} = a.

    According to Newton's Third Law, the magnitude of the force exerted by the car on the truck (FctF_{ct}) is equal to the magnitude of the force exerted by the truck on the car (FtcF_{tc}). Let this magnitude be FF.

    Fct=Ftc=FF_{ct} = F_{tc} = F

    From Newton's Second Law (F=maF = ma):
    For the car: F=mcaracarF = m_{car} a_{car}
    For the truck: F=mtruckatruckF = m_{truck} a_{truck}
    Equating the forces:

    mtruckatruck=mcaracarm_{truck} a_{truck} = m_{car} a_{car}

    Substitute acar=aa_{car} = a:

    mtruckatruck=mcaram_{truck} a_{truck} = m_{car} a

    Solve for atrucka_{truck}:

    atruck=mcarmtruckaa_{truck} = \frac{m_{car}}{m_{truck}} a

    The acceleration that the truck experiences on impact is mcarmtrucka\boxed{\text{}\frac{m_{car}}{m_{truck}} a\text{}}

    Reason: According to Newton's Third Law, the force exerted by the car on the truck is equal in magnitude to the force exerted by the truck on the car. Since the truck typically has a much larger mass than the car (mtruck>mcarm_{truck} > m_{car}), for the same force, the truck's acceleration will be smaller than the car's acceleration.

  2. Determine which driver is likely to be more severely injured and explain why.

    The car driver\boxed{\text{car driver}\text{}} is likely to be more severely injured on impact.

    Explanation:
    During the collision, the less massive car experiences a greater change in velocity (Δv\Delta v) compared to the more massive truck, for the same impulse. Since the time of impact (Δt\Delta t) is the same for both vehicles, the car undergoes a significantly larger deceleration (a=ΔvΔta = \frac{\Delta v}{\Delta t}). This greater deceleration means a larger force is exerted on the car driver by the seatbelt, leading to more severe injuries.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp