Math Problem Statement

Gerak sebuah mahasiswa digambarkan dengan kurva kecepatan seperti di samping. a) Apakah jenis geraknya? b) Tuliskanlah persamaan kecepatan dan persamaan gerak. c) Hitunglah kecepatan dan posisi benda pada 10 sekon.

Solution

From the image you provided, the problem depicts a velocity vs. time graph with the following information:

  • The graph shows a linear increase in velocity from v=2m/sv = 2 \, \text{m/s} at t=0t = 0 seconds to v=8m/sv = 8 \, \text{m/s} at t=5secondst = 5 \, \text{seconds}.

The questions posed are:

(a) What is the type of motion?
The motion is uniformly accelerated because the velocity increases linearly with time.

(b) Write the velocity equation and the motion equation (position equation).

  1. Velocity equation: The slope of the velocity-time graph represents the acceleration, aa.

    The slope

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Math Problem Analysis

Mathematical Concepts

Kinematics
Linear Motion
Uniform Acceleration

Formulas

Velocity equation: v(t) = v_0 + at
Position equation: s(t) = s_0 + v_0t + 0.5at^2

Theorems

Uniformly Accelerated Motion Theorem

Suitable Grade Level

Grades 9-12