
A ball, initially at rest at seconds, rolls with constant acceleration down an inclined plane. If the ball rolls meter in the first seconds, how far will it have rolled at first seconds?
Answer
154.2k+ views
Hint: To solve this question, we have to determine the linear acceleration of the ball from the given information using the second equation of motion. Then, by substituting this value of acceleration in the same equation of motion, we can find out the required displacement of the ball in the first four seconds.
Formula used: The formula used to solve this question is given by
, here is the displacement covered by a particle in the time with a constant acceleration of with an initial velocity of .
Complete step by step solution:
Let the acceleration of the ball be .
As the acceleration of the ball is constant, we can apply the three equations of motion. According to the question, the body covers a displacement of meter in the first seconds. According the second kinematic equation of motion, we have
As the ball is at rest at seconds, so we have . After the first seconds, time elapsed is . Also, displacement covered by the ball during this time is . Substituting these above, we get
On solving we get
………………….(1)
Now, let the displacement of the ball during the first seconds be . Therefore substituting , and in the second equation of motion, we get
The phrase “first seconds” means that time is calculated from seconds. According to the question, the ball is at rest at this instant. So we substitute above to get
From (1)
Hence, the ball has rolled a displacement of in the first four seconds.
Note: We should not worry about the rolling motion of the ball. We have been only asked to find out the linear displacement which the ball has rolled in the given amount of time. The displacement which has been found out is the displacement of the center of mass of the ball.
Formula used: The formula used to solve this question is given by
Complete step by step solution:
Let the acceleration of the ball be
As the acceleration of the ball is constant, we can apply the three equations of motion. According to the question, the body covers a displacement of
As the ball is at rest at
On solving we get
Now, let the displacement of the ball during the first
The phrase “first
From (1)
Hence, the ball has rolled a displacement of
Note: We should not worry about the rolling motion of the ball. We have been only asked to find out the linear displacement which the ball has rolled in the given amount of time. The displacement which has been found out is the displacement of the center of mass of the ball.
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