Question

A computer-controlled racecar is programmed to execute the following motion along the ground for 6.0 seconds. Let’s say the car begins at the origin of our coordinate system. Its initial velocity is ~v0 = (15:0 m/s)^i and its acceleration is constant: ~a = (?6:0 m/s2)^i + (?2:0 m/s2)^j

(a) Make a table, and calculate the car’s position vector, ~r at the end of each second, through t = 6:0 seconds. Use these data to plot the trajectory of the particle for this time interval. You can do it by hand on the axes given to you on the last page. (If you like, you could also do this by writing a computer program that would calculate hundreds of data points).

(b) On your graph, sketch vectors for both the car’s velocity and acceleration at t = 1:0; 2:0 and 4.0 seconds. At each of these instants, is the car speeding up or slowing down? How do you know?

(c) You may have found that judging the answer to part (b) was a tough call for t = 2:0 s. We can do this conclusively: i. Find both the velocity and the speed of the particle at t = 2:0 seconds. ii. At t = 2:0 seconds, find the rate at which the car’s speed is changing (Note that I’m not asking the rate at which its velocity is changing, which is just j~aj). (Hint: you’ll need to find the angle between ~v and ~a, which is something for which the vector dot product is very useful... ) iii. At what time is the rate of change of the car’s speed equal to zero, and what is the car’s speed at this instant? 3

Answer 1

Analysis motion in plane