Maximum Velocity Calculator

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Maximum Velocity Calculator:

Enter the values of mass, m(kg), acceleration, a(m/s2), fluid density, ρ(kg/m3), cross-sectional area, A(m2) and drag coefficient, C to determine the value of maximum velocity, Vmax(m/s).

Enter Mass : kg
Enter Acceleration : m/s2

Enter Fluid Density : kg/m3
Enter Cross-Sectional Area : m2
Enter Drag Coefficient :
   
Result – Maximum Velocity : m/s

Maximum Velocity Formula:

Maximum velocity is the highest speed that an object can reach under specific conditions without further acceleration, typically due to balancing forces like drag against propulsion forces.

Maximum velocity, Vmax(m/s)in metres per seconds is calculated by taking the square root of twice the product of mass, m(kg) in kilograms and acceleration, a(m/s2)in metres per second squared divided by the product of the fluid density, ρ(kg/m3), cross-sectional area, A(m2) and drag coefficient, C.

Maximum velocity, Vmax(m/s) = √( 2 * m(kg) * a(m/s2) / ρ(kg/m3) * A(m2) * C)

Vmax(m/s) = maximum velocity in metres per seconds, m/s.

m(kg) = mass in kilograms, kg.

a(m/s2) = acceleration in metres per second squared, m/s2 (9.81m/s2).

ρ(kg/m3) = fluid density in kilograms per cubic metres, kg/m3.

A(m2) = cross-sectional area in metres square, m2.

C = drag coefficient.

Maximum Velocity Calculation:

1.Determine the maximum velocity of a cyclist with a mass of 80 kg with air density of 1.2 kg/m3, a cross-sectional area of 0.5 m2, and a drag coefficient of 0.9.

Given: m(kg) = 80kg, a(m/s2) = 9.81m/s2, ρ(kg/m3) = 1.2kg/m3, A(m2) = 0.5m2, C = 0.9.

Maximum velocity, Vmax(m/s) = √( 2 * m(kg) * a(m/s2) / ρ(kg/m3) * A(m2) * C)

Vmax(m/s) = √( 2 * 80 * 9.81 / 1.2 * 0.5 * 0.9 )

Vmax(m/s) = √( 1569.6 / 0.54 )

Vmax(m/s) = √2906.7

Vmax(m/s) = 53.9m/s.

2.Calculate the maximum velocity of a sports car with a mass of 1200 kg, accelerating at 3 m/s2, facing air resistance with a fluid density of 1.225 kg/m3, a frontal cross-sectional area of 2.2 m2, and maximum velocity is 97.6m/s.

Given: m(kg) = 1200kg, a(m/s2) = 3m/s2, ρ(kg/m3) = 1.225kg/m3, A(m2) = 2.2m2,

Vmax(m/s) = 97.6m/s.

Maximum velocity, Vmax(m/s) = √( 2 * m(kg) * a(m/s2) / ρ(kg/m3) * A(m2) * C)

C = 2 * m(kg) * a(m/s2) / ρ(kg/m3) * A(m2) * V2max(m/s)

C = 2 * 1200 * 9.81 / 1.225 * 2.2 * 97.62

C = 7200 / 25612.23

C = 0.281.

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