Some of the fastest dragsters do not race for more than 300-400m for safety reasons. Consider such a dragster in this problem, starting a race at rest. After the light turns green, the dragster completes a 400 m race in a time t = 6.8 s.

If the dragster could continue with this average acceleration, what would its speed be, in miles per hour, after it has travelled a total distance of 1.6 km (~ 1 mile) ?

Its speed would be 374.35 miles per hour

Explanation:

For the average acceleration we use 2nd eqn of motion:

s = (Vo) t + at²

Vo = 0 m/s (since, car is initially at rest)

s = 400 m

t = 6.8 s

Therefore, eqn. becomes:

400 m = (0 m/s) (6.8 s) + a (6.8 s) ²

a = 400 m / (6.8 s) ²

a = 8.65 m/s²

Now, for a distance of 1.6 km = 1600 m, with same acceleration, its final speed can be found out by 3rd eqn. of motion:

2as = Vf² - Vo²

2 (8.65 m/s²) (1600 m) = Vf² - (0 m/s) ²

Vf = √27681.66

Vf = 166.38 m/s

Vf = (166.38 m/s) (1 mile/1600 m) (3600 s / 1 hr)

Vf = 374.35 miles per hour