Question

A car starts from 4.0 m/s and travels for 5.0 seconds with a uniform acceleration of 3.0 m/s^2. How far does the car travel during this time?

a. 30 meters
b. 37.5 meters
c. 45 meters
d. 50 meters

Answer 1

Using the equation s = ut + ½at², the distance traveled by the car is found to be 57.5 meters. The available options do not match this result, indicating a potential typo in the options provided.

Step-by-step explanation:

The question asks to calculate the distance traveled by a car that is accelerating uniformly. We can use the kinematic equation for uniformly accelerated linear motion, which is:

s = ut + ½at²

Where:

• s is the displacement (the distance traveled in this context),
• u is the initial velocity (4.0 m/s),
• t is the time (5.0 seconds), and
• a is the acceleration (3.0 m/s²).

Plugging in the values, we get:

s = (4.0 m/s)(5.0 s) + ½(3.0 m/s²)(5.0 s)²

s = 20 m + ½(3.0 m/s²)(25 s²)

s = 20 m + (1.5 m/s²)(25 s²)

s = 20 m + 37.5 m

s = 57.5 m

However, the given options do not include 57.5 meters, implying there may be a typo in the options or the question. Considering the closest correct method, the correct distance traveled is 57.5 meters, not the options provided (a) 30 meters, (b) 37.5 meters, (c) 45 meters, or (d) 50 meters.