Question

Ben Rushin is waiting at a stoplight. When the light turns green, Ben accelerates from rest at a rate of 19.75 m/s^2 for a time of 3.67 seconds. What is Ben's displacement (in meters), and what is his final velocity (in m/s)?

A) Displacement: 134.425 m; Final velocity: 72.2825 m/s

B) Displacement: 52.15825 m; Final velocity: 72.2825 m/s

C) Displacement: 134.425 m; Final velocity: 72.8575 m/s

Answer 1

Ben's displacement is 134.425 m and his final velocity is 72.2825 m/s.

Step-by-step explanation:

To calculate Ben's displacement, we can use the formula:

Displacement = Initial Velocity * Time + (1/2) * Acceleration * Time^2

Given that Ben starts from rest (initial velocity = 0), the equation simplifies to:

Displacement = (1/2) * Acceleration * Time^2

Plugging in the values, the displacement is:

Displacement = (1/2) * 19.75 * 3.67^2 = 134.425 m

Ben's final velocity can be calculated using the formula:

Final Velocity = Initial Velocity + Acceleration * Time

Since Ben starts from rest, the equation simplifies to:

Final Velocity = Acceleration * Time

Plugging in the values, the final velocity is:

Final Velocity = 19.75 * 3.67 = 72.2825 m/s