A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E2.30). (c) What distance does the cat move during the first 4.5 s? From t = 0 to t = 7.5 s?

Question

Velocity-time graph showing a cat's motion with a linear increase in velocity over time.

Accepted Answer

Hey, everybody, let's get into it. So one evening, a lady is strolling along a straight line. The line is along the X axis and to the right is the positive direction you collect data from the ladies motion and construct the graph of velocity as a function of time, determine the lady's acceleration at 1.0 seconds and 3. seconds. Now we are being given a graph of velocity versus time. And the first thing you can note is that because this is a linear function, the velocity is increasing, increasing at a constant rate the whole time, which means the acceleration should also stay constant. Now how do we figure out what her acceleration is? First, we are going to figure out the slope of our line because that's going to give us our change in velocity. So with our why equals MX plus B R linear line, we have, we have acceleration is equal to the change in velocity over the change in time. And that is going to be our slope. And then we just have our plus to be here, which in this case is negative five. So we want to plug in our values here. So the change in velocity um let's pick a nice little triangle to draw. So we will draw, draw a blue triangle right here in order to find our, our slope. So our, our change in speed between these two points starts at negative five and it ends at zero. So our change in speed is going to be zero minus negative five over our value of time. And we're starting out at zero seconds and stopping at 3.5. So at 3.5 seconds minus zero seconds. And if we solve that out, You should get a value of 1.4 m/s. And again, since we have a constant acceleration at 1/2 and 3.5 seconds, we should have the same acceleration. So with our 1.4 m/s, we will go look over our answer choices and answer C A acceleration at time of one second is equal to 1.4 m per second squared. And acceleration at 3.5 seconds also equal to 1.4 m per second squared. Thank you.

Verified Solution

Key Concepts

Velocity

Acceleration

Slope of a Graph