Question

A car has a velocity of 15 meters per second and then accelerates at a uniform rate of 3.5 m per second squared for the next 5.0 seconds. What distance does the car cover during this time? a) 37.5 meters b) 56.25 meters c) 93.75 meters d) 125 meters

Answer 1

The car covers a total distance of 75 meters during the first 5.0 seconds and an additional 43.75 meters during the next 5.0 seconds, the total distance covered by the car during this time is 118.75 meters.

Step-by-step explanation:

To find the distance covered by the car, we need to calculate the area under the velocity-time graph during the given time interval.

First, let's find the distance traveled during the first 5.0 seconds when the car has a constant velocity of 15 m/s.

Since velocity is defined as distance divided by time, the distance covered in this time period is:

Distance = Velocity * Time

Distance = 15 m/s * 5.0 s = 75 meters

Now, let's find the distance covered during the next 5.0 seconds when the car is accelerating at a rate of 3.5 m/s².

We can use the equation of motion:

Distance = Initial Velocity * Time + (1/2) * Acceleration * Time²

Since the initial velocity is 15 m/s, the time is 5.0 seconds, and the acceleration is 3.5 m/s², we can substitute these values into the equation:

Distance = 15 m/s * 5.0 s + (1/2) * 3.5 m/s² * (5.0 s)²

Distance = 75 meters + 43.75 meters = 118.75 meters.

The car covers a total distance of 75 meters during the first 5.0 seconds and an additional 43.75 meters during the next 5.0 seconds.

Therefore, the total distance covered by the car during this time is 75 meters + 43.75 meters = 118.75 meters.