A car moving at 60 km/h applies brakes and comes to a stop in 5 seconds. What is the distance covered during braking?
Practice Questions
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Q1
A car moving at 60 km/h applies brakes and comes to a stop in 5 seconds. What is the distance covered during braking?
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Convert speed to m/s: 60 km/h = 16.67 m/s. Using s = ut + 0.5at², where a = (0 - 16.67)/5 = -3.33 m/s², we find s = 16.67 * 5 + 0.5 * (-3.33) * 5² = 41.67 m.
Questions & Step-by-step Solutions
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Q
Q: A car moving at 60 km/h applies brakes and comes to a stop in 5 seconds. What is the distance covered during braking?
Solution: Convert speed to m/s: 60 km/h = 16.67 m/s. Using s = ut + 0.5at², where a = (0 - 16.67)/5 = -3.33 m/s², we find s = 16.67 * 5 + 0.5 * (-3.33) * 5² = 41.67 m.
Steps: 6
Step 1: Convert the speed from kilometers per hour (km/h) to meters per second (m/s). To do this, use the conversion factor: 1 km/h = 1/3.6 m/s. So, 60 km/h = 60 / 3.6 = 16.67 m/s.
Step 2: Identify the initial speed (u) and the final speed (v). Here, the initial speed u = 16.67 m/s and the final speed v = 0 m/s (since the car stops).
Step 3: Calculate the acceleration (a) using the formula: a = (v - u) / t, where t is the time in seconds. Here, t = 5 seconds. So, a = (0 - 16.67) / 5 = -3.33 m/s².
Step 4: Use the formula for distance (s) covered during braking: s = ut + 0.5at². Substitute the values: s = 16.67 * 5 + 0.5 * (-3.33) * (5)².
Step 5: Calculate the distance: s = 16.67 * 5 = 83.35 m and 0.5 * (-3.33) * 25 = -41.625 m. So, s = 83.35 - 41.625 = 41.725 m.
Step 6: Round the final answer to two decimal places if needed. The distance covered during braking is approximately 41.67 m.
