What is the mass of a car given work and velocity?

[Erenjaeger]

1. The problem statement,
all variables and given/known dataIt takes 190 kJ of work to accelerate a car from 20.8 m/s to 29.3 m/s. What is the car's mass?

Homework Equations

w=fd
f=ma
1/2mv_f²-1/2mv_o²=maΔx=FΔx

The Attempt at a Solution

not sure how to start this problem, because they don't give you time or displacement but you can probably work it out from the velocities I am assuming? just not 100% sure on how to

 

[Orodruin]

Why do you think you need time or displacement?

 

[Erenjaeger]

Why do you think you need time or displacement?

Could you solve by going m=f/a ??

 

[Orodruin]

Could you solve by going m=f/a ??

No. Stop and think a bit about what your relevant equations are telling you about how the input parameters are related to what you want to know.

 

[Erenjaeger]

No. Stop and think a bit about what your relevant equations are telling you about how the input parameters are related to what you want to know.

in the third equation, using energy. Can somehow use that to solve for mass?

 

[Orodruin]

in the third equation, using energy. Can somehow use that to solve for mass?

You tell me. In order to solve for the mass, you need to know all other variables of the equation.

 

[Erenjaeger]

You tell me. In order to solve for the mass, you need to know all other variables of the equation.

the only other variables you need to know are the velocities right? which we are given

 

[Orodruin]

the only other variables you need to know are the velocities right? which we are given

So what is the solution?

 

[Erenjaeger]

So what is the solution?

1/2mv²-1/2mv_o²=190000J
1/2m(20.8m/s)²-1/2m(29.3m/s)² =190000J
1/2m432.64-1/2m858.49=190000J
m⋅216.64-m⋅429.245=190000J
is this correct so far?? not fully sure how to go any further if it is ?

 

[Orodruin]

You are aware that multiplication is distributive, right?
x(y+z) = xy + xz

 

[Erenjaeger]

You are aware that multiplication is distributive, right?
x(y+z) = xy + xz

yeah

 

[haruspex]

1/2m(20.8m/s)2-1/2m(29.3m/s)2 =190000J

The left hand side will clearly be negative, assuming mass is positive.