100A QUIZ 1

1. A man starts running along a square block 1000m on a side. He starts from A and runs one complete round to A, then continues walking to B and stops, as shown. The total time lapse is 35 minutes.  Find (a) his average speed, (b) his average velocity during this time interval. Solution. (a) The total distance covered is             d = (1000m) x 4 + 1000m = 5000m.      We find the average speed from            average speed = d/t = (5000m)/[(35min)(60s/min)] = 2.38m/s. (b) The displacement is Dx = BA = +1000m. (We choose B as positive direction.)      We find the average velocity from              vave = Dx/Dt = (+1000m)/[(35min)(60s/min)] = +0.48m/s.

2. A car accelerates uniformly from rest to 60km/h over a distance of 300m. Find (a) its acceleration, (b) the time it takes during this distance.

Solution.

(a) We find the acceleration from

                   v² = v₀² + 2aDx;

                   [(60km/h)/(3.6ks/h)]² = 0 + 2a(300m), which gives a = 0.46m/s².

(b) We find the time from

                  v = v₀ + at;

                 (60km/h)/(3.6ks/h) = 0 + (0.46)t, which gives t = 36.2s.