Question

A truck is traveling at 22 m/s when the driver notices a speed limit sign for the town ahead. He slows down to a speed of 14 m/s. He travels a distance of 125 m while he is slowing down.

A) Calculate the acceleration of the truck.
B) How long did it take the truck driver to change his speed?

Answer 1

To calculate the truck's acceleration, we use the kinematic equation that relates final velocity, initial velocity, distance, and acceleration. After finding the acceleration, we can then use it to determine the time taken for the truck to slow down.

Step-by-step explanation:

To calculate the acceleration of the truck, we can use the formula for acceleration which is a = (v_f - v_i) / t, where v_f is the final velocity, v_i is the initial velocity, and t is the time taken. But first, we need to find the time using the following kinematic equation: v_f^2 = v_i^2 + 2a d, where a is acceleration and d is the distance.

Step 1: Find the acceleration

We rearrange the equation to solve for acceleration: a = (v_f^2 - v_i^2) / (2d). We plug in the known values: a = (14 m/s)^2 - (22 m/s)^2 / (2 * 125 m), which yields the acceleration.

Step 2: Find the time taken

With the calculated acceleration, we then use the first formula to find the time: t = (v_f - v_i) / a. This gives us the time it took for the truck driver to change his speed.

Answer 2

To determine the acceleration of the truck, we use the kinematic equation which results in -0.768 m/s², indicating deceleration. The time taken to change speed is calculated using the determined acceleration and is found to be 10.42 seconds.

Step-by-step explanation:

To calculate the acceleration of the truck as it slows down, we can use the formula:

a = (vf - vi) / t

where:

• vf is the final velocity (14 m/s),
• vi is the initial velocity (22 m/s), and
• t is the time it takes for the change in velocity to occur

First, we need to rearrange the formula to solve for the acceleration:

a = (14 m/s - 22 m/s) / t

Since we don't have the time t, we use the kinematic equation:

vf2 = vi2 + 2ad

Plugging in the given values and rearranging to solve for a:

a = (vf2 - vi2) / (2d)

a = ((14 m/s)2 - (22 m/s)2) / (2 * 125 m)

a = (-192) / (250)

a = -0.768 m/s2

The negative sign indicates that the truck is decelerating. Now, to find the time t, we can use this acceleration in the equation:

vf = vi + at

Rearrange to solve for t:

t = (vf - vi) / a

t = (14 m/s - 22 m/s) / (-0.768 m/s2)

t = 10.42 seconds

This is the time it took for the truck driver to change his speed.