A race car slows down to make a turn. If it has aninitial velocity of 180 km/h [S] and accelerates at a rateof 8.2 m/s2 [N] for 3.2 s, at what velocity (in kilometresper hour) does the race car make the turn?
Question
A race car slows down to make a turn. If it has aninitial velocity of 180 km/h [S] and accelerates at a rateof 8.2 m/s2 [N] for 3.2 s, at what velocity (in kilometresper hour) does the race car make the turn?
Solution
To solve this problem, we need to convert all the units to the same system. In this case, we will convert everything to the metric system (m/s).
Step 1: Convert the initial velocity from km/h to m/s 180 km/h = 180 * 1000 m/3600 s = 50 m/s
Step 2: Calculate the change in velocity The formula for change in velocity is acceleration * time. So, the change in velocity = 8.2 m/s² * 3.2 s = 26.24 m/s
Step 3: Calculate the final velocity The car is slowing down, so we subtract the change in velocity from the initial velocity. Final velocity = Initial velocity - Change in velocity Final velocity = 50 m/s - 26.24 m/s = 23.76 m/s
Step 4: Convert the final velocity back to km/h 23.76 m/s = 23.76 * 3600 s/1000 m = 85.536 km/h
So, the race car makes the turn at a velocity of approximately 85.536 km/h.
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