Math Problem Statement

In 10 seconds, a car goes from traveling at 20 m/s to 34 m/s. What is the acceleration of the car?

Solution

To solve for the acceleration of the car, we can use the formula:

a=ΔVta = \frac{\Delta V}{t}

Where:

  • ΔV\Delta V is the change in velocity,
  • tt is the time over which this change occurs.

Given:

  • Initial velocity Vi=20m/sV_i = 20 \, \text{m/s},
  • Final velocity Vf=34m/sV_f = 34 \, \text{m/s},
  • Time t=10st = 10 \, \text{s}.

First, we find ΔV\Delta V: ΔV=VfVi=34m/s20m/s=14m/s.\Delta V = V_f - V_i = 34 \, \text{m/s} - 20 \, \text{m/s} = 14 \, \text{m/s}.

Now we calculate the acceleration: a=14m/s10s=1.4m/s2.a = \frac{14 \, \text{m/s}}{10 \, \text{s}} = 1.4 \, \text{m/s}^2.

So, the acceleration of the car is 1.4m/s21.4 \, \text{m/s}^2.

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Math Problem Analysis

Mathematical Concepts

Physics
Kinematics
Acceleration Calculation

Formulas

a = ΔV / t

Theorems

Definition of Acceleration

Suitable Grade Level

Grades 9-11