Q63P - University Physics with Modern Physics

Question

A ball starts from rest and rolls down a hill with uniform acceleration, traveling 200 m during the second 5.0 s of its motion. How far did it roll during the first 5.0 s of motion?

Step-by-Step Solution

Answer

the ball rolled 500 m during the first of motion 5.0 s.

Step 1: Identification of the given data

The given data can be expressed below as:

• The ball travels about 200 m.
• Both the first and the second motion of the ball occurred in 5.0 s.

Step 2: Significance of the Newton’s first law to find the motion

This law illustrates that an object will continue to move in a uniform motion unless an external force acts upon the object.

The equation of velocity gives the acceleration of the ball and the equation of displacement gives the distance the ball rolled.

Step 3: Determination of the distance the ball rolled

From the Newton’s first law, the equation of velocity of the ball is expressed as:

v = u + at

Here, v is the final velocity of the ball which is 150 m/s, u is the initial velocity of the ball which is zero as the ball was at rest and t is the time taken for rolling the ball.

Substituting the values in the above expression, we get-

$$\begin{gathered} 200 m/s=0+\left(5.0s\right)a \\ a=40 m/s^2 \end{gathered}$$

Hence, the equation of the displacement of the ball along a straight line is expressed as:

$s=ut+05a{t}^2$

Substituting the values in the above expression, we get-

$$\begin{gathered} s=0+0.5\times 40 m/s^2\times {\left(5\right)}^2 \\ =500 m \end{gathered}$$

Thus, the ball rolled during the first of motion 500 m.