Question

A porsche challenges a honda to a 400 m race. because the porsche's acceleration of 3.5 m/s2is larger than the honda's 3.0 m/s2, the honda gets a 1.0 s head start. who wins?

Answer 1

D = distance to be traveled by each porsche and honda in the race = 400 m

for porsche :

a = acceleration = 3.5 m/s²

t = time of travel = ?

v₀ = initial velocity = 0 m/s

Using the equation

D = v₀ t + (0.5) a t²

inserting the values

400 = 0 t + (0.5) (3.5)t²

t = 15.12 sec

for honda :

for first 1 sec :

d = distance traveled in first 1 sec

a' = acceleration = 3 m/s²

t' = time of travel = ?

v'₀ = initial velocity = 0 m/s

using the equation

d = v'₀ t' + (0.5) a' t'²

d = (0) (1) + (0.5) (3) (1)²

d = 1.5 m

velocity gained after 1 sec :

v' = v'₀  + a' t'

v' = 0 + (3 x 1) = 3 m/s

D' = distance travelled by honda during race = D - d' = 400 - 1.5 = 398.5 m

t'' = time taken to travel the remaining distance = ?

v' = initial velocity for remaining distance = 3 m/s

a' = acceleration = 3 m/s²

using the equation

D' = v' t'' + (0.5) a' t''²

398.5 = 3 t'' +  (0.5) (3) t''²

t'' = 15.32 sec

since the time taken by honda is larger . hence porshce wins