Answer Happy

Question 1 A tortoise and hare get into a race. However, hare as usual gets into napping under the tree and when he gets up, he realizes that he is only 60 m away from the finish line. He looks around for the tortoise who was 59.5 m ahead of him and diligently grinding along at his best speed of 0.11 m/s. The bewildered hare accelerates at 4 m/s^2 up to his top speed of 18 m/s and sustains that speed till finish line Hint: Read the problem again and understand we are comparing 2 objects moving a certain distance at different speeds and accelerations. Write all 5 variables for 2 objects and all 3 equations for 2 objects. How can you figure out, using the equations for each object, who would reach the finish line first. Will you compare their velocities or displacements, or time needed to complete the leftover distance to finish line. Once you figure this out, solve for that variable for both animals. That will help you determine who wins the race. Remember hare can accelerate till he reaches 18 m/s and then moves at constant velocity till the end. The hare has two segments of motion with acceleration and then no acceleration.
Question 2 A test vehicle on a straight track begins a run starting from rest at t=0. It subsequently has an acceleration versus time curve that starts with a linear increase and then levels of after 10 s at 5 m/s^2 a. Draw the a(t) Vs. t graph for 0-12 seconds using above info and label. Use linear equation formula to write equations of acceleration for the two sections. b. Determine the 2 equations for v(t) during the time interval 0 ≤t≤ 10s and 10-12s. c. Remember to integrate the acceleration equation. d. Determine the position X(t) equation for the motion if the object was 8 m away at t=0s. Remember to integrate Velocity equations. e. What is the location of the test vehicle at t=12 s, f. Sketch V-T graph for 1-12 s g. Sketch X-T graph for 1-12 s