Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 101

Bobsled acceleration. In the start of a four-person bobsled race, two drivers (a pilot and a brakeman) are already on board while two pushers accelerate the sled along the ice by pushing against the ice with spiked shoes. After pushing for 50 m along a straight course, the pushers jump on board. The acceleration during the pushing largely determines the time to slide through the rest of the course and thus decides the winner with the least run time, which often depends on differences of 1.0 ms. Consider an x axis along the 50 m, with the origin at the start position. If the position x versus time t in the pushing phase is given by \(x = 0.3305t^2 + 4.2060t\) (in meters and seconds), then at the end of a 9.000 s push what are (a) the speed and (b) the acceleration?