Rank the following sports cars by the net force required to produce the given mo

Question

Rank the following sports cars by the net force required to produce the given motion. Assume a constant acceleration for each car. A Lamborghini Gallardo of mass m 1430 kg Largest Net Force starts with a speed of 9.16 m/s and goesa distance of d = 102 m in a time of t = 4.25 s. A Bugatti Veyron of mass m 1890 kg goes from 6.93 to 29.3 m/s over a distance of d 40.5 m A Dodge Viper of mass mo = 1570 kg goes from 6.93 to 38.2 m/s in a time of t = 4.08 s. Smallest Net Force A Nissan GT-R of mass mN 1680 kg goes from 11.2 to 38.8 m/s over a distance of d 68.8 m. issanLamborghini Dodge Bugat GTRGallardoViperVeyron net

Explanation / Answer

here,

for Lamborghini

m1 = 1430 kg

initial speed , u1 = 9.16 m/s

distance travelled , s1 = 102 m

t1 = 4.25 s

let the accelration be a1

s1 = u1 * t1 + 0.5 * a1 * t1^2

102 = 9.16 * 4.25 + 0.5 * a1 + 4.25^2

solving for a1

a1 = 6.98 m/s^2

force , F1 = m1 * a1 = 9986 N

for Bugatti veyron

m2 = 1890 kg

initial speed , u2 = 6.93 m/s

distance travelled , s2 = 40.5 m

v = 38.2 m/s

let the accelration be a2

v^2 - u2^2 = 2 * a2 * s2

38.2^2 - 6.93^2 = 2 * a2 * 40.5

a2 = 17.4 m/s^2

force , F2 = m2 * a2 = 32928 N

for Dodge Viper

m3 = 1570 kg

initial speed , u3 = 6.93 m/s

v3 = 38.2 m/s

t3 = 4.08 s

let the accelration be a3

v3 = u3 + a3 * t3

38.2 = 6.93 + a3 * 4.08

a3 = 7.66 m/s^2

force , F3 = m3 * a3 = 12032 N

for Nissan GT-R

m4 = 1680 kg

u4 = 11.2 m/s

v4 = 38.8 m/s

s4 = 68.8 m

let the accelration be a4

v4^2 - u4^2 = 2 * s4 * a4

38.8^2 - 11.2^2 = 2 * 68.8 * a4

a4 = 10 m/s^2

the force , F4 = m4*a4 = 16848 N

so, the ranking of cars is

Bugatti veyron > Nissan GT-R > Dodge Viper > Lamborghini

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