Question

Consider a car that is initially traveling along a straight stretch of highway at 15 m/s. At t=0 the car begins to accelerate at 2.0 m/s^2 in order to pass a truck. The final velocity is vx=25m/s. Calculate how far the car travels during its 5.0 s of acceleration.A) If the car maintains its constant acceleration for a total time of 15 s , what total distance does it travel?Express your answer in meters to the nearest integer.

Answer 1

The car travels 100 m during the 5.0 s of acceleration.

The distance traveled after 15 s with constant acceleration is 450 m

Step-by-step explanation:

Hi there!

The equation of position of the car at a time t is the following:

x = x0 + v0 · t + 1/2 · a · t²

Where:

x = position of the car at a time t.

x0 = initial position.

v0 = initial velocity.

t = time.

a = acceleration.

Let's place the origin of the frame of reference at the point where the car starts accelerating so that x0 = 0. The final position of the car will be equal to the traveled distance:

x = v0 · t + 1/2 · a · t²

Let's calculate the traveled distance after 5.0 s:

x = 15 m/s · 5.0 s + 1/2 · 2.0 m/s² · (5.0 s)²

x = 100 m

The car travels 100 m during the 5.0 s of acceleration.

Now, let's calculate the traveled distance of the car if it continues accelerating at 2.0 m/s² for a total time 15 s:

x = v0 · t + 1/2 · a · t²

x = 15 m/s · 15 s + 1/2 · 2.0 m/s² · (15 s)²

x = 450 m

The distance traveled after 15 s with constant acceleration is 450 m.