Determine from the graph the speed of the car

[songoku]

Homework Statement

A toy car of mass 0.5 kg works with a wound spring that exerts a force as shown in the table below.The car was initially at rest. The spring is wound at the car set in motion on a horizontal surface.

t = 0 s ------> F = 0.2 N
t = 1 s ------> F = 0.18 N
t = 2 s ------> F = 0.15 N
t = 3 s ------> F = 0.12 N
t = 4 s ------> F = 0.1 N
t = 5 s ------> F = 0.08 N
t = 6 s ------> F = 0.05 N
t = 7 s ------> F = 0.02 N
t = 8 s ------> F = 0 N

a. Plot the graph of force vs time using the table above. Determine from the graph the speed of the car 8 s after being released.

b. The car then crashes into a stationary car of mass 1.5 kg and is stuck to the second car. Calculate the speed of the two cars after collision. Show if the collision is elastic or not

Homework Equations

1. p = Ft
2. conservation of momentum

3. attempt at a solution
a.

I'm not sure how to find the speed from the graph. The best I can try is I assume the graph is triangle, then I find the area which is equal to change in momentum.

Area = change in momentum
0.5*0.2*8 = mv
v = 1.6 ms^-1


b. m₁u₁+m₂u₂=(m₁+m₂)V
0.5*1.6 = (0.5 + 1.5) V
V = 0.4 ms^-1

The collision is perfectly inelastic

Am I right ?

Thanks

 

[rock.freak667]

your theory looks correct to me.

 

[songoku]

Hi rock.freak667

Thanks a lot !