A car accelerates from rest at a rate of 3 m/s² for 10 seconds, then maintains a constant speed of 30 m/s for another 20 seconds. Calculate the total distance traveled during this time.
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To calculate the total distance traveled, we need to find the distances covered during the acceleration phase and the constant speed phase separately, and then add them together.
During the acceleration phase, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given:
initial velocity = 0 m/s (starting from rest)
acceleration = 3 m/s²
time = 10 seconds
distance = (0 * 10) + (0.5 * 3 * 10^2)
distance = 0 + 0.5 * 3 * 100
distance = 0 + 0.5 * 300
distance = 0 + 150
distance = 150 meters
During the constant speed phase, the car maintains a speed of 30 m/s for 20 seconds. To find the distance covered, we can use the formula:
distance = speed * time
Given:
speed = 30 m/s
time = 20 seconds
distance = 30 * 20
distance = 600 meters
Therefore, the total distance traveled during this time period is 150 meters + 600 meters = 750 meters.
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