In 1898, the world land speed record was set by Gaston Chasseloup-Laubat driving

Question

In 1898, the world land speed record was set by Gaston Chasseloup-Laubat driving a car named Jeantaud. His speed was 39.24 mph (63.15 km/h), much lower than the limit on our interstate highways today. Repeat the calculations of Example 2.7 (assume the car accelerates for 6 miles to get up to speed, is then timed for a one-mile distance, and accelerates for another 6 miles to come to a stop) for the Jeantaud car. (Assume the car moves in the +x direction.) (a) Find the acceleration for the first 6 miles. 0.015 m/s2 (b) How long did the Jeantaud take to cover the timed mile? 91.742 (c) What was the acceleration for the last 6 miles? 0.02 m/s

Explanation / Answer

Here ,

a) distance traveled for acceleration , d = 6 miles = 6 * 1609 m

final speed , v = 63.15 km/hr = 17.54 m/s

a) for the acceleration

a = v^2/(2 * d)

a = 17.54^2/(2 * 6 * 1609)

a = 0.15 m/s^2

b)

for the timed mile

time taken = distance/speed

time taken = 1609/17.54

time taken = 91.7 s

c) for the deceleration also,

as the distance taken is same , using third equation of motion

v^2 - u^2 = 2 *a *d

a = - 17.54^2/(2 * 6 * 1609)

a = - 0.16 m/s^2

the acceleration is - 0.16 m/s^2

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