A car travels from rest with a constant acceleration a for t seconds. What is the average speedof the car for its journey, if the car moves along a straight road?(A) at2/2 (B) 2at2 (c)at/2 (D) None
Question
A car travels from rest with a constant acceleration a for t seconds. What is the average speedof the car for its journey, if the car moves along a straight road?(A) at2/2 (B) 2at2 (c)at/2 (D) None
Solution
The average speed of an object moving at a constant acceleration is given by the formula:
Average speed = Total distance / Total time
In this case, the car starts from rest and moves with a constant acceleration 'a' for 't' seconds. The total distance covered by the car is given by the equation of motion:
Distance = Initial velocity * time + 0.5 * acceleration * (time)^2
Since the car starts from rest, the initial velocity is zero. So, the equation simplifies to:
Distance = 0.5 * a * t^2
Substituting this into the formula for average speed gives:
Average speed = (0.5 * a * t^2) / t = 0.5 * a * t
So, the average speed of the car for its journey is 0.5 * a * t, which is not listed in the options. Therefore, the correct answer is (D) None.
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