Question

If you let a ball roll down a nearly flat, 25-meter-long ramp, how long will it take to reach the end of the ramp if it accelerates at 0.5 (m/s)²}?

a. 10 seconds
b. 5 seconds
c. 7 seconds
d. 2 seconds

Answer 1

To determine the time it takes for a ball to roll down a ramp with constant acceleration, we apply the kinematic formula d = vit + (1/2)at². With the acceleration given as 0.5 m/s² and the displacement as 25 meters, the solution is 10 seconds.

Step-by-step explanation:

To solve how long it will take a ball to reach the end of a ramp when it accelerates at 0.5 (m/s)², we can use the kinematic equation for uniformly accelerated motion:

• d = vit + (1/2)at²

Where d is the displacement (25 meters), vi is the initial velocity (0 m/s, since the ball starts from rest), a is the acceleration (0.5 m/s²), and t is the time. Plugging in the values:

• 25 m = (0 m/s)(t) + (1/2)(0.5 m/s²)(t²)

This simplifies to:

• 25 m = (0.25 m/s²)(t²)

Divide both sides by 0.25 m/s²:

• 100 = t²

Take the square root of both sides:

• t = 10 s

The correct answer is 10 seconds. Thus, option (a) is correct.