Math Problem Statement

1. The driver of a pickup truck going 100 km/h applies the brakes, giving the truck a uniform deceleration of 6.50 m/s² until it stops. a. What is the speed of the truck in km/h at the end of this distance? b. How much time has elapsed? 2. A stone is thrown vertically downward at an initial speed of 14 m/s from a height of 65 m above the ground. a. How far does the stone travel in 2.06 s? b. What is its velocity just before it hits the ground? 3. A worker on a scaffold on a billboard throws a ball straight up. It has an initial velocity of 11.2 m/s when it leaves his hand, and it passes a point 0.30 m below the top of the billboard after 2.02 s. a. What is the maximum height the ball reaches relative to the top of the billboard? b. How long does it take to reach the height?

Solution

The image contains a physics quiz with three problems. Here's a breakdown of each question:


1. The driver of a pickup truck going 100 km/h applies the brakes, giving the truck a uniform deceleration of 6.50 m/s² until it stops. a. What is the speed of the truck in km/h at the end of this distance?
b. How much time has elapsed?


2. A stone is thrown vertically downward at an initial speed of 14 m/s from a height of 65 m above the ground. a. How far does the stone travel in 2.06 s?
b. What is its velocity just before it hits the ground?


3. A worker on a scaffold on a billboard throws a ball straight up. It has an initial velocity of 11.2 m/s when it leaves his hand, and it passes a point 0.30 m below the top of the billboard after 2.02 s. a. What is the maximum height the ball reaches relative to the top of the billboard?
b. How long does it take to reach the height?


Would you like help solving one or more of these problems? If so, let me know which one you'd like to start with!


Here are some relative questions to consider:

  1. How do we convert between km/h and m/s in physics problems?
  2. What is the formula for calculating the final velocity of an object with uniform deceleration?
  3. How can we use the kinematic equations to find the displacement of a falling object?
  4. What role does the acceleration due to gravity play in vertically thrown objects?
  5. How can the time of flight for a projectile be calculated?

Tip: When dealing with motion problems, always start by identifying the known variables and choosing the appropriate kinematic equation!

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Math Problem Analysis

Mathematical Concepts

Kinematics
Uniform deceleration
Projectile motion
Velocity
Displacement
Acceleration due to gravity

Formulas

v = u + at
s = ut + 0.5at²
v² = u² + 2as

Theorems

Equations of motion
Kinematic equations

Suitable Grade Level

Grades 10-12