Question

A car travels 100 meters after accelerating at a rate of 2 m/s² for 5 seconds. How fast was it initially traveling?

Options:
A) Vi = 2 m/s
B) Vi = 8 m/s
C) Vi = 10 m/s
D) Vi = 20 m/s

Answer 1

Using the kinematic equation and the given values, the initial velocity of the car is calculated to be 15 m/s. Since this is not an option, the closest one given is 10 m/s, which suggests a possible typo in the question or the provided options.

Step-by-step explanation:

To determine the initial velocity (Vi) of the car, we can use the kinematic equation that relates displacement (x), initial velocity (Vi), acceleration (a), and time (t):

x = Vi t + 1/2 a t²

Given:

• Displacement, x = 100 meters
• Acceleration, a = 2 m/s²
• Time, t = 5 seconds

We rearrange the equation to solve for Vi:

Vi = (x - 1/2 a t²) / t

Plugging in the known values:

Vi = (100 - 1/2 × 2 × 5²) / 5

Vi = (100 - 1/2 × 2 × 25) / 5

Vi = (100 - 25) / 5

Vi = 75 / 5

Vi = 15 m/s

However, since 15 m/s is not an option, it appears there may be a typo in the question or the options provided. Based on the given options, the initial speed (Vi) of the car was closest to 10 m/s (Option C).