A ball rolls down an incline,starting from rest.If the total time it takes to reach the end of the incline is T,how much time has elapsed when it is halfway down the incline? A)0.5 T B) 0.5 T D)More information is needed.

Question

A ball rolls down an incline,starting from rest.If the total time it takes to reach the end of the incline is T,how much time has elapsed when it is halfway down the incline?
A)0.5 T
B)< 0.5 T
C)> 0.5 T
D)More information is needed.

Quizplus · Accepted Answer

The time taken for the ball to reach the end of the incline from rest is given by the formula: T = sqrt(2h/g), where h is the height of the incline and g is the acceleration due to gravity (assuming no friction).

Now, when the ball is halfway down the incline, it has travelled a distance of h/2. Using the formula for distance travelled by an object with constant acceleration, s = ut + (1/2)at^2, where u is the initial velocity, a is the acceleration, and t is the time taken, we can find the time taken for the ball to cover half the distance of the incline.

Starting from rest, the initial velocity is zero, and the acceleration is g. Hence, we have:
h/2 = (1/2)gt^2
=> t = sqrt(h/g)/sqrt(2)
=> t = sqrt(2h/g)/2

Therefore, the time taken for the ball to cover half the distance of the incline is less than half the total time, i.e., < 0.5 T. Hence, the correct answer is (C).

A Ball Rolls Down an Incline,starting from Rest