Antiderivatives

Question

A car is traveling at 86 km/h when the driver sees an accident 70 m ahead and slams on the brakes. What minimum constant deceleration is required to stop the car in time to avoid a pileup? (Round your answer to two decimal places.)

Answer 1

If we want to state the deceleration in m/s², we should convert the speed of the car to m/s

86 km/hr * 1 hr/3600 s * 1000 m/km = 86000/3600 m/s = 860/36 m/s = 215/9 m/s

Then, 1/2 at² = 70

at = 215/9

1/2 t = 70/(215/9)

t = 252/43 s

a = at/t

a = 215/9/(252/43) = 43 * 215/ (9 * 252 ) = 9245/2268 m/s² = 4.08 m/s²

If you want to mix units, you can multiply by 3600/1000 = 18/5 and have km/hr/sec