6. A car accelerates from rest at 4.3 m/s^2 for 4 s (Segment 1), travels at a co

Question

6. A car accelerates from rest at 4.3 m/s^2 for 4 s (Segment 1), travels at a constant speed for 7 s (Segment 2), accelerates at 1.0 m/s^2 for 16 s (Segment 3), and then decelerates to rest at 2.9 m/s^2 (Segment 4). The figure below describes the motion but not to scale. How far has the ear traveled? Do this problem in stages, determining the distance traveled during each of the four segments and then summing. Segment 1: Distance in Segment 1= Segment 2: Distance in Segment 2= Segment 3: Distance in Segment 3= Segment 4: Distance in Segment 4 = Total

Explanation / Answer

Here ,

for sagment 1 ,

d1 = 0.5 * a*t^2

d1 = 0.5 * 4.3 * 4^2

d1 = 34.4 m

for sagment 2 ,

d2 = speed * time

d2 = 4.3 * 4 * 7

d2 = 120.4 m

for sagment 3 ,

using second equation of motion

d3 = 4.3 * 4 * 16 + 0.5 * 1 * 16^2

d3 = 403.2 m

for sagment 4 ,

using third equation of motion

d4 = (4.3 * 4 + 16 *1)^2/(2 * 2.9)

d4 = 190 m

total distance = 34.4 + 120.4 + 403.2 + 190

total distance = 748 m

the total distance travelled is 748 m

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