An object is moving in a straight line.At t = 0,its speed is 5.0 m/s.From t = 0 to t = 4.0 s,its acceleration is 2.5 m/s².From t = 4.0 s to t = 11.0 s,its speed is constant.The average speed over the entire time interval is A)9.5 m/s B)15 m/s C)13 m/s D)21 m/s E)8.2 m/s

Question

Quizplus · Accepted Answer

First, we need to find the final speed of the object at t = 4.0 s using the equation of motion:

v = u + at

where v is the final speed, u is the initial speed, a is the acceleration, and t is the time interval.

v = 5.0 + 2.5(4.0) = 15.0 m/s

From t = 4.0 s to t = 11.0 s, the speed is constant, so the distance traveled during this time interval is:

distance = speed x time = 15.0 x (11.0-4.0) = 105.0 m

From t = 0 to t = 4.0 s, we can use the equation of motion again to find the distance traveled:

distance = ut + 0.5at^2 = 5.0(4.0) + 0.5(2.5)(4.0)^2 = 50.0 m

Therefore, the total distance traveled over the entire time interval is:

total distance = 50.0 + 105.0 = 155.0 m

And the total time taken is:

total time = 11.0 s

So, the average speed is:

average speed = total distance / total time = 155.0 / 11.0 = 14.1 m/s ≈ 13 m/s (rounded to one significant figure)

Therefore, the best choice is C.

An Object Is Moving in a Straight Line