Let's break down and solve the problem step by step: --- ### **Step 1: Understand the Problem** You are asked to **sketch the v vs t graph** (velocity vs time) for an object whose displacement as a function of time is given by a previous problem (Trig 2-44). The **velocity** is defined as: \[ \text{velocity} = \frac{\text{change in distance}}{\text{change in time}} \] --- ### **Step 2: Review the Calculations** You have calculated average velocities for different intervals: a) \( v = \frac{2.5}{10} = 0.25 \) b) \( v = \frac{16}{30} = 0.53 \) c) \( v = \frac{20}{40} = 0.5 \) d) \( v = \frac{10}{50} = 0.2 \) e) \( v = \frac{6}{20} = 0.3 \) --- ### **Step 3: Assign Times to Each Interval** Each velocity calculation seems to represent the average velocity over a specific time interval. Let's assign the midpoint of each interval as the time associated with each calculated velocity. - For \( \frac{2.5}{10} \), midpoint is \( t = 5 \) - For \( \frac{16}{30} \), midpoint is \( t = 15 \) - For \( \frac{20}{40} \), midpoint is \( t = 20 \) - For \( \frac{10}{50} \), midpoint is \( t = 25 \) - For \( \frac{6}{20} \), midpoint is \( t = 10 \) Let’s arrange all data (time, velocity): - (5, 0.25) - (10, 0.3) - (15, 0.53) - (20, 0.5) - (25, 0.2) --- ### **Step 4: Sketch the v vs t Graph** Now, plot these points (time on x-axis, velocity on y-axis): - At \( t = 5 \), \( v = 0.25 \) - At \( t = 10 \), \( v = 0.3 \) - At \( t = 15 \), \( v = 0.53 \) - At \( t = 20 \), \( v = 0.5 \) - At \( t = 25 \), \( v = 0.2 \) Connect these points smoothly to approximate the v vs t graph. --- ### **Step 5: Final Answer** #### **Table of Values:** | Time (t) | Velocity (v) | |----------|--------------| | 5 | 0.25 | | 10 | 0.3 | | 15 | 0.53 | | 20 | 0.5 | | 25 | 0.2 | #### **Graph:** On the graph provided: - Mark each point from the table. - Connect the points with a smooth curve or straight lines. --- ### **Explanation** These velocities are **average velocities** over each interval. By plotting them against the midpoint of each time interval, you get an approximate v-t graph for the object's motion as described by the displacement function. --- ### **Final Answer Summary** - **Table of velocities at intervals is above.** - **Graph is sketched by plotting these points and connecting them.** - **The shape of the curve gives insight into how the object's velocity changes with time.** If you need a more detailed plot or have the explicit displacement function from Trig 2-44, you could compute the instantaneous velocity at each point using calculus (derivative). For now, this is an approximate, step-by-step solution based on your data!