A car starts from point P at time t=0 and travels at 45 mph.
A)write an expression d(t) for the distance the car travels from p. (would it just be y=45x??)
B)What is the slope of the graph? what does it have to do with the Car?
D)Create a scenario in which t could have negative values
E)create a scenario in which the y-intercept of y-d(t) could be 30.
Hey, how come no one has answered parts c through e? I need some help here!!! This is the ONLY site on the internet that has this problem worked.
a. correct, but I would do it this way:
d(t)=45mph* t where t is in hours.
b. slope is 45mph
A) To write an expression for the distance the car travels from point P, you can use the equation for distance, which is given by d = rt, where d is the distance, r is the rate or speed, and t is the time.
In this case, the car is traveling at a speed of 45 mph. So, the expression for the distance traveled, d(t), would be:
d(t) = 45t
B) The slope of the graph represents the rate at which the distance is changing with respect to time. In this case, the slope is 45, which means that for every unit of time (t), the car travels 45 units of distance (d).
The slope of 45 is directly related to the car because it represents the car's constant speed, which is 45 mph. Therefore, the slope of the graph is the same as the car's speed.
C) The given scenario assumes that the car starts from point P at time t=0. In this situation, time cannot have negative values because it is measured from the starting point at t=0. However, we can create a scenario where the distance traveled can have negative values.
For example:
Let's say that the car starts from point P at time t=5 and travels at a speed of 45 mph. In this case, the expression for the distance traveled, d(t), would be:
d(t) = 45(t - 5)
Here, for any value of t less than 5, the distance traveled would be negative because the car has not yet reached the starting point at t=5.
D) To create a scenario where the y-intercept of y = d(t) could be 30, we need to set the distance traveled at time t=0 equal to 30.
For example:
Let's say the car starts at point P at time t=0 and has an initial burst of speed that covers a distance of 30 units. After that, it travels at a constant speed of 45 mph. The expression for the distance traveled, d(t), would be:
d(t) = 30 + 45t
In this scenario, the y-intercept (the distance traveled at t=0) is 30, which means that when time is 0, the car has already covered a distance of 30 units.
A) To write an expression for the distance the car travels from point P at time t, you can use the formula:
d(t) = speed * time
In this case, the speed of the car is 45 mph, and time is represented by t. Therefore, the expression for the distance traveled, d(t), would be:
d(t) = 45 * t
B) The slope of the graph represents the rate of change of the distance with respect to time. In this scenario, the slope is 45. This means that for every unit increase in time, the car travels 45 units in distance. The slope being equal to the speed (45 mph) indicates that the car maintains a constant speed throughout the journey.
D) A scenario in which time (t) could have negative values is if you consider the car starting its journey from a point P in the past and moving towards the present. For example, let's say the car started at t=-1 hour from the present moment, and the current time is t=0. In this case, as time progresses towards the present (t=0), the car's distance will increase.
E) To create a scenario where the y-intercept of y-d(t) could be 30, you need to consider a situation where the car has traveled a certain distance before time t=0. For example, if the car has already traveled 30 miles before starting from point P at t=0, then the y-intercept (distance at time t=0) would be 30. The expression for this scenario would be:
d(t) = 45t + 30