A car travelling on a straight track accelerates uniformly from rest for 5.0 s and then travels at a constant speed for the next 5.0 s, covering a total distance of 75 m in that time. Determine the constant speed that the car achieved.
A) 7.5 m/s
B) 10 m/s
C) 15 m/s
D) 20 m/s
E) 30 m/s
thanks bobpursley the correct answer is 10m/s i just didn't know how they got it. I Presumed that they were talking about the entire 10 seconds.
To determine the constant speed that the car achieved, we need to use the equation for distance traveled during uniformly accelerated motion:
d = v0t + 0.5at^2
In this case, the car accelerates uniformly from rest, so its initial velocity (v0) is 0. The time for the first part of the motion is 5.0 s. Therefore, the equation simplifies to:
d = 0.5at^2
Since there is no acceleration during the second part of the motion (constant speed), we can calculate the distance traveled during that time as well:
d = vt
Given that the total distance is 75 m and the time for the second part is also 5.0 s, we can add the two distances to get:
75 = 0.5at^2 + vt
Now, let's solve for the constant speed:
75 = 0.5at^2 + vt
As we have no information about acceleration, let's assume it as "a". Our equation now becomes:
75 = 0.5at^2 + v(t + 5)
Let's isolate the constant speed term:
75 = 0.5at^2 + vt + 5v
Since the car travels at a constant speed during the second part of the motion, the term 0.5at^2 becomes 0. Therefore:
75 = vt + 5v
Rearranging the terms:
75 = 5v + vt
Dividing both sides of the equation by 5:
15 = v + t
We know that t = 5.0 s, so let's substitute that value:
15 = v + 5.0
Subtracting 5.0 from both sides:
10 = v
Therefore, the constant speed that the car achieved is 10 m/s.
So, the correct answer is B) 10 m/s.
I wonder if "convering a total distance in that time" refers to the entire 10 seconds, or the last five seconds.
if the last five seconds
v=75/5=25m/s
if the entire ten seconds,
distance during the first five seconds is V/2 * 5=2.5V
75=2.5V+5V or V=10m/s