Comparing Distances in Sport & Automobiles

[Rylynn97]

1. A sport car starting from rest can attain a speed of 60 mi/hr in 8s. A runner can do a 100-yd dash in 9.8s. Assume that the runner is moving with a constant speed and that the car starts at the instant he passes it. How far will both travel until the car overtakes the runner? (convert distances to ft, time to s)

2. An automobile traveling 56 km/hr is 24m from a barrier when the driver slams on the brakes. The car hits the barrier two seconds later. (a) What was the car's deceleration before the impact? (b) How fast was the car traveling at impact? (distances to m, time to s)

Help?

 

[dimensionless]

1.

What is the cars acceleration? Find equations for both the positions of both the car and the runner as functions of time. They should intersect at t=0 and t= t2, where t2 is the time at which the car overtakes the runner. Then find how far the runner has traveled at t=t2.

2.

Given that the decelleration is a, integrate it to find an equation for the velocity v(t) that meets the initial condition of v(0) = 56 km/hr. Integrate the velocity equation to get an equation for the distance x(t) that meets the boundary conditions x(0) = 0 and x(2s) = 24 m.