A train moving with a speed of 60 km/h applies brakes and comes to a stop in 5 seconds. What is the magnitude of its acceleration?
Practice Questions
1 question
Q1
A train moving with a speed of 60 km/h applies brakes and comes to a stop in 5 seconds. What is the magnitude of its acceleration?
-3 m/s²
-2 m/s²
-1 m/s²
-4 m/s²
First, convert speed to m/s: 60 km/h = 60/3.6 = 16.67 m/s. Using the formula: acceleration = (final velocity - initial velocity) / time = (0 - 16.67) / 5 = -3.33 m/s², approximately -3 m/s².
Questions & Step-by-step Solutions
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Q
Q: A train moving with a speed of 60 km/h applies brakes and comes to a stop in 5 seconds. What is the magnitude of its acceleration?
Solution: First, convert speed to m/s: 60 km/h = 60/3.6 = 16.67 m/s. Using the formula: acceleration = (final velocity - initial velocity) / time = (0 - 16.67) / 5 = -3.33 m/s², approximately -3 m/s².
Steps: 6
Step 1: Convert the speed from kilometers per hour (km/h) to meters per second (m/s). 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 velocity (u) and final velocity (v). The initial velocity (u) is 16.67 m/s (the speed of the train), and the final velocity (v) is 0 m/s (the train stops).
Step 3: Use the formula for acceleration (a): a = (v - u) / t, where t is the time taken to stop. Here, t = 5 seconds.
Step 4: Substitute the values into the formula: a = (0 - 16.67) / 5.
Step 5: Calculate the acceleration: a = -16.67 / 5 = -3.33 m/s².
Step 6: The magnitude of acceleration is the absolute value, which is approximately 3 m/s².
