kloseyq

Answered

2022-01-12

A Honda Civic travels in a straight line along a road. The car’s distance x from a stop sign is given as a function of time t by the equation $x\left(t\right)=\alpha {t}^{2}-\beta {t}^{3}$ , where $\alpha =1.50\text{}\frac{m}{{s}^{2}}$ and $\beta =0.0500\text{}\frac{m}{{s}^{3}}$

Calculate the average velocity of the car for each time interval:

a)$t=0$ to $t=2.00s$

b)$t=0$ to $t=4.00\text{}s$

c)$t=2.00s$ to $t=4.00s$

Calculate the average velocity of the car for each time interval:

a)

b)

c)

Answer & Explanation

chumants6g

Expert

2022-01-13Added 33 answers

Step 1

First we have to calculate the distance x at each t.

$x\left(0\right)=\text{Zero}\text{}m$

$x\left(2\right)=1.50{\left(2\right)}^{2}-0.0500{\left(2\right)}^{3}=5.6m$

$x\left(4\right)=1.50{\left(4\right)}^{2}-0.0500{\left(4\right)}^{3}=20.8m$

The average velocity is the displacement divided by the time interval at which this displacement happened.

$v}_{x,\text{}avg}=\frac{\mathrm{\Delta}x}{\mathrm{\Delta}t$

$\mathrm{\Delta}x={x}_{f}-{x}_{i}$

$\mathrm{\Delta}t={t}_{f}-{t}_{i}$

Step 2

a)$v}_{x,\text{}avg}=\frac{{x}_{f}-{x}_{i}}{{t}_{f}-{t}_{i}$

$x\left(0\right)=\text{Zero}\text{}m$

$x\left(2\right)=1.50{\left(2\right)}^{2}-0.0500{\left(2\right)}^{3}=5.6m$

$v}_{x,\text{}avg}=\frac{5.6-0}{2-0$

$=2.8ms$

Step 3

b)$x\left(0\right)=\text{Zero}\text{}m$

$x\left(4\right)=1.50{\left(4\right)}^{2}-0.0500{\left(4\right)}^{3}=20.8m$

$v}_{x,\text{}avg}=\frac{20.8-0}{4-0$

$=5.2ms$

Step 4

c)$x\left(2\right)=1.50{\left(2\right)}^{2}-0.0500{\left(2\right)}^{3}=5.6m$

$x\left(4\right)=1.50{\left(4\right)}^{2}-0.0500{\left(4\right)}^{3}=20.8m$

$v}_{x,\text{}avg}=\frac{20.8-5.6}{4-2$

$=7.6ms$

First we have to calculate the distance x at each t.

The average velocity is the displacement divided by the time interval at which this displacement happened.

Step 2

a)

Step 3

b)

Step 4

c)

Mary Herrera

Expert

2022-01-14Added 37 answers

Step 1

a) The equation for cars

a) The equation for cars

nick1337

Expert

2022-01-14Added 573 answers

Step 1

a) The position of the car as a function of time t is given by

where

The average velocity is given by the ratio between the displacement and the time taken:

The position at t = 0 is:

The position at t = 2.00 s is:

So the displacement is

The time interval is

And so, the average velocity in this interval is

b) The position at t = 0 is:

While the position at t = 4.00 s is:

So the displacement is

The time interval is

So the average velocity here is

c) The position at t = 2 s is:

While the position at t = 4 s is:

So the displacement is

While the time interval is

So the average velocity is

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