Need someone to check my work and answers:
At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 2.80 m/s2. At the same instant a truck, traveling with a constant speed of 20.0 m/s, overtakes and passes the car.
(a) How far beyond its starting point does the car overtake the truck?
20t = 1.40t²
cancel "t"
1.40t = 20
t = 20/1.4 = 14.3s
distance at overtake = 20(14.3) = 286 m ANS-1
(b) How fast is the car traveling when it overtakes the truck?
auto's speed at any time = t is
V = 2.80t = 2.80(14.3) = 40 m/s m/s ANS-2
-For part (c) and (d) of the question, can you explain how the graph for both parts would look like and how you got it.
(c)Draw the correct x−t graph of the motion of both vehicles.
(d)Draw the correct vx−t graph of the motion of both vehicles.
looks good...except for the word "cancel t" in (a). variables cannot "cancel" out, what you did was divide each side by t to reduce it to 1.40t=20
To answer part (c) and (d), we can first analyze the motion of both vehicles separately.
For the car:
The car starts from rest and accelerates at a constant rate of 2.80 m/s^2. This means its velocity increases linearly with time. Therefore, its position-time graph (x-t graph) will be a curved line with increasing slope.
For the truck:
The truck travels with a constant speed of 20.0 m/s. Since the truck's velocity remains constant, its position-time graph will be a straight line with a constant slope.
Now let's discuss how to draw the velocity-time graph (v-t graph) for both vehicles.
For the car:
The car's velocity is given by V = at, where a is the acceleration and t is the time. In this case, the acceleration is constant at 2.80 m/s^2. So, the car's velocity-time graph will be a straight line with a slope of 2.80 m/s^2.
For the truck:
The truck travels with a constant speed of 20.0 m/s, which means its velocity-time graph will be a horizontal line at 20.0 m/s.
In summary:
(c) The position-time graph will have a curved line for the car (increasing slope) and a straight line for the truck (constant slope).
(d) The velocity-time graph will have a straight line with a slope of 2.80 m/s^2 for the car and a horizontal line at 20.0 m/s for the truck.
To accurately draw these graphs, you can label the axes (x or t on the horizontal axis, and x or t on the vertical axis for the position-time graph, and v or t on the horizontal axis, and v on the vertical axis for the velocity-time graph). Then plot the corresponding points based on the description given above.