The velocity-versus-time graph is shown for a particle moving along the x-axis. Its initial position is x0 = 1.8m at t0 =0s.
Part A
What is the particle's position at t=1.0s?
Part B
What is the particle's acceleration at t= 1.0s?
Part C
What is the particle's position at
t= 3.0s?
Part D
What is the particle's acceleration at t= 3.0s?
3.8m
what are the answers
To answer these questions, we need to analyze the velocity-versus-time graph. Let's break it down step-by-step:
Part A:
To find the particle's position at t = 1.0s, we need to find the area under the velocity-versus-time graph from t = 0 to t = 1.0s. The area under the graph represents the displacement of the particle.
Since the shape of the graph is a triangle, we can find the area by calculating the area of the triangle.
Step 1: Find the base of the triangle:
The base of the triangle is the time interval from t = 0 to t = 1.0s, which is 1.0s - 0s = 1.0s.
Step 2: Find the height of the triangle:
The height of the triangle is the velocity at t = 1.0s.
Step 3: Calculate the area of the triangle:
The area of a triangle is given by the formula: Area = (1/2) * base * height.
Solving for the area, we get:
Area = (1/2) * 1.0s * (velocity at t = 1.0s)
Part B:
To find the particle's acceleration at t = 1.0s, we need to look at the slope of the velocity-versus-time graph at that specific time. The slope of a velocity-versus-time graph represents the acceleration.
Step 1: Look at the graph and find the slope at t = 1.0s. The slope can be determined by the steepness of the line at that specific time.
Part C:
To find the particle's position at t = 3.0s, we need to find the area under the velocity-versus-time graph from t = 0 to t = 3.0s. The process is similar to Part A.
Step 1: Find the base of the triangle:
The base of the triangle is the time interval from t = 0 to t = 3.0s, which is 3.0s - 0s = 3.0s.
Step 2: Find the height of the triangle:
The height of the triangle is the velocity at t = 3.0s.
Step 3: Calculate the area of the triangle:
The area of a triangle is given by the formula: Area = (1/2) * base * height.
Solving for the area, we get:
Area = (1/2) * 3.0s * (velocity at t = 3.0s)
Part D:
To find the particle's acceleration at t = 3.0s, we need to look at the slope of the velocity-versus-time graph at that specific time. The process is similar to Part B.
To find the answers to these questions, we can analyze the given velocity-versus-time graph and use the equations of motion.
Here's how you can find the answers:
Part A:
To find the particle's position at t = 1.0s, we need to find the area under the velocity-versus-time graph up to t = 1.0s. This area represents the displacement of the particle.
Step 1: Locate the point on the graph corresponding to t = 1.0s.
Step 2: Identify the region under the graph up to t = 1.0s.
Step 3: Calculate the area of this region.
Step 4: The calculated area represents the displacement of the particle from its initial position. Adding this displacement to the initial position x0 will give us the particle's position at t = 1.0s.
Part B:
To find the particle's acceleration at t = 1.0s, we can calculate the slope of the velocity-versus-time graph at that specific time.
Step 1: Locate the point on the graph corresponding to t = 1.0s.
Step 2: Draw a tangent line at this point.
Step 3: Calculate the slope of the tangent line, which represents the particle's acceleration at t = 1.0s.
Part C:
To find the particle's position at t = 3.0s, we can again use the area under the velocity-versus-time graph. This time, we need to find the total area up to t = 3.0s.
Step 1: Locate the point on the graph corresponding to t = 3.0s.
Step 2: Identify the region under the graph up to t = 3.0s.
Step 3: Calculate the total area of this region.
Step 4: As before, adding this calculated area to the initial position x0 will give us the particle's position at t = 3.0s.
Part D:
To find the particle's acceleration at t = 3.0s, we can again calculate the slope of the velocity-versus-time graph at that specific time.
Step 1: Locate the point on the graph corresponding to t = 3.0s.
Step 2: Draw a tangent line at this point.
Step 3: Calculate the slope of the tangent line, which represents the particle's acceleration at t = 3.0s.
By following these steps and analyzing the velocity-versus-time graph, you can find the answers to each part of the question.