A car that slows down uniformly from 20 m/s to 5 m/s has an impulse of 30,000 kg m/s. Determine the mass of the car
M*V1 + M*V2 = 30,000
V1 = 20 m/s
V2 = 5 m/s
Solve for M.
Complete solution
The impulse is given by the formula:
Impulse = Mass × Change in Velocity
We are given the impulse (30,000 kg m/s) and the change in velocity (20 m/s - 5 m/s = 15 m/s).
Plugging in these values into the formula, we have:
30,000 kg m/s = Mass × 15 m/s
To solve for the mass of the car, we isolate the Mass:
Mass = Impulse / Change in Velocity
Mass = 30,000 kg m/s / 15 m/s
Mass = 2000 kg
Therefore, the mass of the car is 2000 kg.
To find the mass of the car, we can use the formula for impulse:
Impulse = force * change in time
However, in this case, we don't have the force or the change in time. We only have the initial velocity, final velocity, and impulse.
To solve this problem, we can use the equation of motion:
Impulse = mass * change in velocity
Rearranging the equation, we can solve for mass:
mass = impulse / change in velocity
Given:
Initial velocity (u) = 20 m/s
Final velocity (v) = 5 m/s
Impulse = 30,000 kg m/s
Change in velocity (Δv) = v - u
Substituting the values:
mass = 30,000 kg m/s / (5 m/s - 20 m/s)
mass = 30,000 kg m/s / (-15 m/s)
mass = -30,000 kg m/s / 15 m/s
mass = -2000 kg
However, mass cannot be negative. Negative mass does not make sense in this context.
Therefore, there might be an error or a misunderstanding in the given information. Please double-check the values provided.